Electrochromic multi-layer devices with spatially coordinated switching

ABSTRACT

A multi-layer device comprising a first substrate and a first electrically conductive layer on a surface thereof, the first electrically conductive layer having a sheet resistance to the flow of electrical current through the first electrically conductive layer that varies as a function of position.

FIELD OF THE INVENTION

The present invention generally relates to switchable electrochromicdevices, such as architectural windows, capable of coordinated switchingover substantially their entire area or a selected subregion of theirentire area. More particularly, and in one preferred embodiment, thepresent invention is directed to switchable electrochromic multi-layerdevices, particularly large area rectangular windows for architecturalapplications that switch in a spatially coordinated manner oversubstantially their entire area or a selected subregion of their entirearea; optionally these are of non-uniform shape, optionally they switchsynchronously, i.e., uniformly, over substantially their entire area ora selected subregion of their entire area, or in a coordinated butnonsynchronous manner (e.g., from side-to-side, or top-to-bottom) from afirst optical state, e.g., a transparent state, to a second opticalstate, e.g., a reflective or colored state.

BACKGROUND OF THE INVENTION

Commercial switchable glazing devices are well known for use as mirrorsin motor vehicles, automotive windows, aircraft window assemblies,sunroofs, skylights, architectural windows. Such devices may comprise,for example, inorganic electrochromic devices, organic electrochromicdevices, switchable mirrors, and hybrids of these having two conductinglayers with one or more active layers between the conducting layers.When a voltage is applied across these conducting layers the opticalproperties of a layer or layers in between change. Such optical propertychanges are typically a modulation of the transmissivity of the visibleor the solar subportion of the electromagnetic spectrum. Forconvenience, the two optical states will be referred to as a lightenedstate and a darkened state in the following discussion, but it should beunderstood that these are merely examples and relative terms (i.e., oneof the two states is “lighter” or more transmissive than the otherstate) and that there could be a set of lightened and darkened statesbetween the extremes that are attainable for a specific electrochromicdevice; for example, it is feasible to switch between intermediatelightened and darkened states in such a set.

Switching between a lightened and a darkened state in relatively smallelectrochromic devices such as an electrochromic rear-view mirrorassembly is typically quick and uniform, whereas switching between thelightened and darkened state in a large area electrochromic device canbe slow and spatially non-uniform. Gradual, non-uniform coloring orswitching is a common problem associated with large area electrochromicdevices. This problem, commonly referred to as the “iris effect,” istypically the result of the voltage drop through the transparentconductive coatings providing electrical contact to one side or bothsides of the device. For example, when a voltage is initially applied tothe device, the potential is typically the greatest in the vicinity ofthe edge of the device (where the voltage is applied) and the least atthe center of the device; as a result, there may be a significantdifference between the transmissivity near the edge of the device andthe transmissivity at the center of the device. Over time, however, thedifference in applied voltage between the center and edge decreases and,as a result, the difference in transmissivity at the center and edge ofthe device decreases. In such circumstances, the electrochromic mediumwill typically display non-uniform transmissivity by initially changingthe transmissivity of the device in the vicinity of the appliedpotential, with the transmissivity gradually and progressively changingtowards the center of the device as the switching progresses. While theiris effect is most commonly observed in relatively large devices, italso can be present in smaller devices that have correspondingly higherresistivity conducting layers.

SUMMARY OF THE INVENTION

Among the various aspects of the present invention is the provision ofrelatively large-area electrochromic multi-layer devices capable ofcoordinated switching and coloring, across substantially its entire areathat can be easily manufactured.

Briefly, therefore, the present invention is directed to a multi-layerdevice comprising a first substrate and a first electrically conductivelayer on a surface thereof. The first electrically conductive layer istransmissive to electromagnetic radiation having a wavelength in therange of infrared to ultraviolet and has a sheet resistance, R_(s), tothe flow of electrical current through the first electrically conductivelayer that varies as a function of position in the first electricallyconductive layer wherein the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least 2.

Another aspect of the present invention is a multi-layer devicecomprising a first substrate and a first electrically conductive layeron a surface thereof. The first electrically conductive layer has aspatially varying sheet resistance, R_(s), to the flow of electricalcurrent through the first electrically conductive layer that varies as afunction of position in the first electrically conductive layer whereinthe ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in the first electricallyconductive layer is at least about 1.25.

Another aspect of the present invention is a multi-layer devicecomprising a first substrate, a first electrically conductive layer on asurface of that substrate, and a first electrode layer on a surface ofthe first electrically conductive layer. The first electricallyconductive layer has a spatially varying sheet resistance, R_(s), thatvaries as a function of position in the first electrically conductivelayer wherein the ratio of the value of maximum sheet resistance,R_(max), to the value of minimum sheet resistance, R_(min), in the firstelectrically conductive layer is at least about 1.25.

Another aspect of the present invention is a multi-layer devicecomprising a first substrate and a first electrically conductive layeron a surface of the substrate. The first electrically conductive layerhas a spatially varying sheet resistance, R_(s), that varies as afunction of position in the first electrically conductive layer whereina contour map of the sheet resistance, R_(s), as a function of positionwithin the first electrically conductive layer contains a set ofisoresistance lines and a set of resistance gradient lines normal to theisoresistance lines. The sheet resistance along a gradient line in theset generally increases, generally decreases, generally increases untilit reaches a maximum and then generally decreases, or generallydecreases until it reaches a minimum and then generally increases. Inone embodiment, for example, the gradient in sheet resistance is aconstant. By way of further example, in one embodiment, the gradient insheet resistance is a constant and the substrate is rectangular inshape.

Another aspect of the present invention is a multi-layer devicecomprising a first substrate, a first electrically conductive layer on asurface of the substrate, and a first electrode layer on a surface ofthe first electrically conductive layer. The first electricallyconductive layer has a spatially varying sheet resistance, R_(s), thatvaries as a function of position in the first electrically conductivelayer wherein a contour map of the sheet resistance, R_(s), as afunction of position within the first electrically conductive layercontains a set of isoresistance lines and a set of resistance gradientlines normal to the isoresistance lines. The sheet resistance along agradient line in the set generally increases, generally decreases,generally increases until it reaches a maximum and then generallydecreases, or generally decreases until it reaches a minimum and thengenerally increases. In one embodiment, for example, the gradient insheet resistance is a constant. By way of further example, in oneembodiment, the gradient in sheet resistance is a constant and thesubstrate is rectangular in shape

Another aspect of the present invention is an electrochromic multi-layerdevice comprising an electrochromic layer between and in electricalcontact with a first and a second electrically conductive layer. Thefirst and/or second electrically conductive layers have a spatiallyvarying sheet resistance, R_(s), that varies as a function of positionin the first and/or second electrically conductive layer(s) wherein acontour map of the sheet resistance, R_(s), as a function of positionwithin the first and/or second electrically conductive layer(s) containsa set of isoresistance lines and a set of resistance gradient linesnormal to the isoresistance lines. The sheet resistance along a gradientline in the first and/or second electrically conductive layer(s)generally increase(s), generally decrease(s), generally increase(s)until it reaches a maximum and then generally decrease(s), or generallydecrease(s) until it reaches a minimum and then generally increase(s).In one embodiment, for example, the gradient in sheet resistance is aconstant. By way of further example, in one embodiment, the gradient insheet resistance is a constant and the substrate is rectangular in shape

A further aspect of the present invention is an electrochromic devicecomprising a first substrate, a first electrically conductive layer, afirst electrode layer, a second electrically conductive layer and asecond substrate. The first and second electrically conductive layerseach have a sheet resistance, R_(s), to the flow of electrical currentthrough the first and second electrically conductive layers that variesas a function of position in the first and second electricallyconductive layers, respectively, wherein the ratio of the value ofmaximum sheet resistance, R_(max), to the value of minimum sheetresistance, R_(min), in the first electrically conductive layer is atleast 2 and the ratio of the value of maximum sheet resistance, R_(max),to the value of minimum sheet resistance, R_(min), in the secondelectrically conductive layer is at least 2. The first substrate and thefirst electrically conductive layer are transmissive to electromagneticradiation having a wavelength in the range of infrared to ultraviolet.For example, in one embodiment the first substrate and the firstelectrically conductive layer are transparent to electromagneticradiation having a wavelength in the range of infrared to ultraviolet.

A further aspect of the present invention is a process for modulatingthe transmissivity of an electrochromic multi-layer device, themulti-layer device comprising an electrochromic layer between and inelectrical contact with a first and a second electrically conductivelayer. The process comprises applying a voltage pulse between the firstand second electrically conductive layers, the voltage pulse having amagnitude of at least about 2 volts. The voltage pulse induces theelectrochromic layer to switch from a first to a second optical statewherein the first or second optical state has a greater transmissivityto electromagnetic radiation having a wavelength in the range ofultraviolet to infrared wavelengths relative to the other optical state,and the second optical state persists at least 1 second after the pulseand in the absence of a voltage applied between the electricallyconductive layers.

A further aspect of the present invention is a process for thepreparation of a multi-layer device, the process comprises forming afirst electrically conductive layer on a surface of a first substrate.The first electrically conductive layer comprises a transparentconductor and has a spatially varying sheet resistance, R₈, to the flowof electrical current through the first electrically conductive layerthat varies as a function of position in the first electricallyconductive layer wherein the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 1.25

A further aspect of the present invention is a process for thepreparation of a multi-layer device. The process comprises forming amultilayer structure comprising an electrochromic layer, an electricallyconductive layer and a substrate, the electrically conductive layerbeing between the first electrode layer and the substrate. The firstelectrically conductive layer has a spatially varying sheet resistance,R_(s), to the flow of electrical current through the first electricallyconductive layer that varies as a function of position in the firstelectrically conductive layer wherein the ratio of the value of maximumsheet resistance, R_(max), to the value of minimum sheet resistance,R_(min), in the first electrically conductive layer is at least about1.25

A further aspect of the present invention is directed to a process forthe preparation of a multi-layer device. The process comprises forming amulti-layer layer structure comprising an electrochromic layer betweenand in electrical contact with a first and a second electricallyconductive layer. The first and/or the second electrically conductivelayer has a spatially varying sheet resistance, R_(s), to the flow ofelectrical current through the first and/or the second electricallyconductive layer that varies as a function of position in the firstand/or the second electrically conductive layer, respectively, whereinthe ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in the first and/or thesecond electrically conductive layer is at least about 1.25,respectively.

Other objects and features will be in part apparent and in part pointedout hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-section of a multi-layer electrochromicdevice of the present invention.

FIG. 2A-2E is a series of contour maps of the sheet resistance, R_(s),in the first and/or second electrically conductive layer as a functionof position (two-dimensional) within the first and/or secondelectrically conductive layer showing isoresistance lines (alsosometimes referred to as contour lines) and resistance gradient lines(lines perpendicular to the isoresistance lines) resulting from variousalternative arrangements of bus bars for devices having square andcircular perimeters.

FIG. 3 is a schematic cross-section of an electrically conductive layerhaving a graded thickness on a substrate.

FIG. 4 is a schematic cross-section of an alternative embodiment of amulti-layer electrochromic device of the present invention.

FIG. 5 is a 1-D lumped element circuit model diagram used to simulatedynamic behavior of an electrochromic device as described in Example 1.

FIG. 6 is plot of the voltage waveform applied to the bus bars asdescribed in Example 1.

FIG. 7 is plot of current flowing into the device versus time asdescribed in Example 1.

FIG. 8 is plot of the voltage across the electrochromic film at threelocations (near the edge, near the center, and between these two) asdescribed in Example 1.

FIG. 9 is plot of the voltage waveform applied to the bus bars asdescribed in Example 1.

FIG. 10 is plot of current flowing into the device versus time asdescribed in Example 1.

FIG. 11 is plot of the voltage across the electrochromic film at threelocations (near the edge, near the center, and between these two) asdescribed in Example 1.

FIG. 12 is a 1-D lumped element circuit model diagram used to simulatedynamic behavior of an electrochromic device as described in Example 2.

FIG. 13 is plot of the voltage waveform applied to the bus bars asdescribed in Example 1.

FIG. 14 is plot of current flowing into the device versus time asdescribed in Example 1.

FIG. 15 is plot of the voltage across the electrochromic film at threelocations (near the edge, near the center, and between these two asdescribed in Example 1.

FIG. 16 is a 1-D lumped element circuit model diagram used to simulatedynamic behavior of an electrochromic device as described in Example 3.

FIG. 17 is plot of the voltage waveform applied to the bus bars asdescribed in Example 1.

FIG. 18 is plot of current flowing into the device versus time asdescribed in Example 1.

FIG. 19 is plot of the voltage across the electrochromic film at threelocations (near the edge, near the center, and between these two) asdescribed in Example 1.

FIG. 20 is a schematic cross-section of an alternative embodiment of amulti-layer electrochromic device of the present invention.

FIG. 21 is an exploded view of the multi-layer device of FIG. 1.

Corresponding reference characters indicate corresponding partsthroughout the drawings. Additionally, relative thicknesses of thelayers in the different figures do not represent the true relationshipin dimensions. For example, the substrates are typically much thickerthan the other layers. The figures are drawn only for the purpose toillustrate connection principles, not to give any dimensionalinformation.

ABBREVIATIONS AND DEFINITIONS

The following definitions and methods are provided to better define thepresent invention and to guide those of ordinary skill in the art in thepractice of the present invention. Unless otherwise noted, terms are tobe understood according to conventional usage by those of ordinary skillin the relevant art.

The term “anodic electrochromic layer” refers to an electrode layer thatchanges from a more transmissive state to a less transmissive state uponthe removal of ions.

The term “cathodic electrochromic layer” refers to an electrode layerthat changes from a more transmissive state to a less transmissive stateupon the insertion of ions.

The terms “conductive” and “resistive” refer to the electricalconductivity and electrical resistivity of a material.

The term “convex polygon” refer to a simple polygon in which everyinternal angle is less than or equal to 180 degrees, and every linesegment between two vertices remains inside or on the boundary of thepolygon. Exemplary convex polygons include triangles, rectangles,pentagons, hexagons, etc., in which every internal angle is less than orequal to 180 degrees and every line segment between two vertices remainsinside or on the boundary of the polygon.

The term “electrochromic layer” refers to a layer comprising anelectrochromic material.

The term “electrochromic material” refers to materials that are able tochange their optical properties, reversibly, as a result of theinsertion or extraction of ions and electrons. For example, anelectrochromic material may change between a colored, translucent stateand a transparent state.

The term “electrode layer” refers to a layer capable of conducting ionsas well as electrons. The electrode layer contains a species that can beoxidized when ions are inserted into the material and contains a speciesthat can be reduced when ions are extracted from the layer. This changein oxidation state of a species in the electrode layer is responsiblefor the change in optical properties in the device.

The term “electrical potential,” or simply “potential,” refers to thevoltage occurring across a device comprising an electrode/ionconductor/electrode stack.

The term “transmissive” is used to denote transmission ofelectromagnetic radiation through a material.

The term “transparent” is used to denote substantial transmission ofelectromagnetic radiation through a material such that, for example,bodies situated beyond or behind the material can be distinctly seen orimaged using appropriate image sensing technology.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 depicts a cross-sectional structural diagram of electrochromicdevice 1 according to a first embodiment of the present invention.Moving outward from the center, electrochromic device 1 comprises an ionconductor layer 10. First electrode layer 20 is on one side of and incontact with a first surface of ion conductor layer 10, and secondelectrode layer 21 is on the other side of and in contact with a secondsurface of ion conductor layer 10. In addition, at least one of firstand second electrode layers 20, 21 comprises electrochromic material; inone embodiment, first and second electrode layers 20, 21 each compriseelectrochromic material. The central structure, that is, layers 20, 10,21, is positioned between first and second electrically conductivelayers 22 and 23 which, in turn, are arranged against outer substrates24, 25. Elements 22, 20, 10, 21, and 23 are collectively referred to asan electrochromic stack 28.

Electrically conductive layer 22 is in electrical contact with oneterminal of a power supply (not shown) via bus bar 26 and electricallyconductive layer 23 is in electrical contact with the other terminal ofa power supply (not shown) via bus bar 27 whereby the transmissivity ofelectrochromic device 10 may be changed by applying a voltage pulse toelectrically conductive layers 22 and 23. The pulse causes electrons andions to move between first and second electrode layers 20 and 21 and, asa result, electrochromic material in the first and/or second electrodelayer(s) change(s) optical states, thereby switching electrochromicdevice 1 from a more transmissive state to a less transmissive state, orfrom a less transmissive state to a more transmissive state. In oneembodiment, electrochromic device 1 is transparent before the voltagepulse and less transmissive (e.g., more reflective or colored) after thevoltage pulse or vice versa.

It should be understood that the reference to a transition between aless transmissive and a more transmissive state is non-limiting and isintended to describe the entire range of transitions attainable byelectrochromic materials to the transmissivity of electromagneticradiation. For example, the change in transmissivity may be a changefrom a first optical state to a second optical state that is (i)relatively more absorptive (i.e., less transmissive) than the firststate, (ii) relatively less absorptive (i.e., more transmissive) thanthe first state, (iii) relatively more reflective (i.e., lesstransmissive) than the first state, (iv) relatively less reflective(i.e., more transmissive) than the first state, (v) relatively morereflective and more absorptive (i.e., less transmissive) than the firststate or (vi) relatively less reflective and less absorptive (i.e., moretransmissive) than the first state. Additionally, the change may bebetween the two extreme optical states attainable by an electrochromicdevice, e.g., between a first transparent state and a second state, thesecond state being opaque or reflective (mirror). Alternatively, thechange may be between two optical states, at least one of which isintermediate along the spectrum between the two extreme states (e.g.,transparent and opaque or transparent and mirror) attainable for aspecific electrochromic device. Unless otherwise specified herein,whenever reference is made to a less transmissive and a moretransmissive, or even a bleached-colored transition, the correspondingdevice or process encompasses other optical state transitions such asnon-reflective-reflective, transparent-opaque, etc. Further, the term“bleached” refers to an optically neutral state, e.g., uncolored,transparent or translucent. Still further, unless specified otherwiseherein, the “color” of an electrochromic transition is not limited toany particular wavelength or range of wavelengths. As understood bythose of skill in the art, the choice of appropriate electrochromic andcounter electrode materials governs the relevant optical transition.

In general, the change in transmissivity preferably comprises a changein transmissivity to electromagnetic radiation having a wavelength inthe range of infrared to ultraviolet radiation. For example, in oneembodiment the change in transmissivity is predominately a change intransmissivity to electromagnetic radiation in the infrared spectrum. Ina second embodiment, the change in transmissivity is to electromagneticradiation having wavelengths predominately in the visible spectrum. In athird embodiment, the change in transmissivity is to electromagneticradiation having wavelengths predominately in the ultraviolet spectrum.In a fourth embodiment, the change in transmissivity is toelectromagnetic radiation having wavelengths predominately in theultraviolet and visible spectra. In a fifth embodiment, the change intransmissivity is to electromagnetic radiation having wavelengthspredominately in the infrared and visible spectra. In a sixthembodiment, the change in transmissivity is to electromagnetic radiationhaving wavelengths predominately in the ultraviolet, visible andinfrared spectra.

The materials making up electrochromic stack 28 may comprise organic orinorganic materials, and they may be solid or liquid. For example, incertain embodiments the electrochromic stack 28 comprises materials thatare inorganic, solid (i.e., in the solid state), or both inorganic andsolid. Inorganic materials have shown better reliability inarchitectural applications. Materials in the solid state can also offerthe advantage of not having containment and leakage issues, as materialsin the liquid state often do. It should be understood that any one ormore of the layers in the stack may contain some amount of organicmaterial, but in many implementations one or more of the layers containslittle or no organic matter. The same can be said for liquids that maybe present in one or more layers in small amounts. In certain otherembodiments some or all of the materials making up electrochromic stack28 are organic. Organic ion conductors can offer higher mobilities andthus potentially better device switching performance. Organicelectrochromic layers can provide higher contrast ratios and morediverse color options. Each of the layers in the electrochromic deviceis discussed in detail, below. It should also be understood that solidstate material may be deposited or otherwise formed by processesemploying liquid components such as certain processes employing sol-gelsor chemical vapor deposition.

Referring again to FIG. 1, the power supply (not shown) connected to busbars 26, 27 is typically a voltage source with optional current limitsor current control features and may be configured to operate inconjunction with local thermal, photosensitive or other environmentalsensors. The voltage source may also be configured to interface with anenergy management system, such as a computer system that controls theelectrochromic device according to factors such as the time of year,time of day, and measured environmental conditions. Such an energymanagement system, in conjunction with large area electrochromic devices(e.g., an electrochromic architectural window), can dramatically lowerthe energy consumption of a building.

At least one of the substrates 24, 25 is preferably transparent, inorder to reveal the electrochromic properties of the stack 28 to thesurroundings. Any material having suitable optical, electrical, thermal,and mechanical properties may be used as first substrate 24 or secondsubstrate 25. Such substrates include, for example, glass, plastic,metal, and metal coated glass or plastic. Non-exclusive examples ofpossible plastic substrates are polycarbonates, polyacrylics,polyurethanes, urethane carbonate copolymers, polysulfones, polyimides,polyacrylates, polyethers, polyester, polyethylenes, polyalkenes,polyimides, polysulfides, polyvinylacetates and cellulose-basedpolymers. If a plastic substrate is used, it may be barrier protectedand abrasion protected using a hard coat of, for example, a diamond-likeprotection coating, a silica/silicone anti-abrasion coating, or thelike, such as is well known in the plastic glazing art. Suitable glassesinclude either clear or tinted soda lime glass, including soda limefloat glass. The glass may be tempered or untempered. In someembodiments of electrochromic device 1 with glass, e.g. soda lime glass,used as first substrate 24 and/or second substrate 25, there is a sodiumdiffusion barrier layer (not shown) between first substrate 24 and firstelectrically conductive layer 22 and/or between second substrate 25 andsecond electrically conductive layer 23 to prevent the diffusion ofsodium ions from the glass into first and/or second electricallyconductive layer 23. In some embodiments, second substrate 25 isomitted.

In one preferred embodiment of the invention, first substrate 24 andsecond substrate 25 are each float glass. In certain embodiments forarchitectural applications, this glass is at least 0.5 meters by 0.5meters, and can be much larger, e.g., as large as about 3 meters by 4meters. In such applications, this glass is typically at least about 2mm thick and more commonly 4-6 mm thick.

Independent of application, the electrochromic devices of the presentinvention may have a wide range of sizes. In general, it is preferredthat the electrochromic device comprise a substrate having a surfacewith a surface area of at least 0.001 meter². For example, in certainembodiments, the electrochromic device comprises a substrate having asurface with a surface area of at least 0.01 meter². By way of furtherexample, in certain embodiments, the electrochromic device comprises asubstrate having a surface with a surface area of at least 0.1 meter².By way of further example, in certain embodiments, the electrochromicdevice comprises a substrate having a surface with a surface area of atleast 1 meter². By way of further example, in certain embodiments, theelectrochromic device comprises a substrate having a surface with asurface area of at least 5 meter². By way of further example, in certainembodiments, the electrochromic device comprises a substrate having asurface with a surface area of at least 10 meter².

At least one of the two electrically conductive layers 22, 23 is alsopreferably transparent in order to reveal the electrochromic propertiesof the stack 28 to the surroundings. In one embodiment, electricallyconductive layer 23 is transparent. In another embodiment, electricallyconductive layer 22 is transparent. In another embodiment, electricallyconductive layers 22, 23 are each transparent. In certain embodiments,one or both of the electrically conductive layers 22, 23 is inorganicand/or solid. Electrically conductive layers 22 and 23 may be made froma number of different transparent materials, including transparentconductive oxides, thin metallic coatings, networks of conductive nanoparticles (e.g., rods, tubes, dots) conductive metal nitrides, andcomposite conductors. Transparent conductive oxides include metal oxidesand metal oxides doped with one or more metals. Examples of such metaloxides and doped metal oxides include indium oxide, indium tin oxide,doped indium oxide, tin oxide, doped tin oxide, zinc oxide, aluminumzinc oxide, doped zinc oxide, ruthenium oxide, doped ruthenium oxide andthe like. Transparent conductive oxides are sometimes referred to as(TCO) layers. Thin metallic coatings that are substantially transparentmay also be used. Examples of metals used for such thin metalliccoatings include gold, platinum, silver, aluminum, nickel, and alloys ofthese. Examples of transparent conductive nitrides include titaniumnitrides, tantalum nitrides, titanium oxynitrides, and tantalumoxynitrides. Electrically conducting layers 22 and 23 may also betransparent composite conductors. Such composite conductors may befabricated by placing highly conductive ceramic and metal wires orconductive layer patterns on one of the faces of the substrate and thenover-coating with transparent conductive materials such as doped tinoxides or indium tin oxide. Ideally, such wires should be thin enough asto be invisible to the naked eye (e.g., about 100 μm or thinner).Non-exclusive examples of electron conductors 22 and 23 transparent tovisible light are thin films of indium tin oxide (ITO), tin oxide, zincoxide, titanium oxide, n- or p-doped zinc oxide and zinc oxyfluoride.Metal-based layers, such as ZnS/Ag/ZnS and carbon nanotube layers havebeen recently explored as well. Depending on the particular application,one or both electrically conductive layers 22 and 23 may be made of orinclude a metal grid.

The thickness of the electrically conductive layer may be influenced bythe composition of the material comprised within the layer and itstransparent character. In some embodiments, electrically conductivelayers 22 and 23 are transparent and each have a thickness that isbetween about 1000 nm and about 50 nm. In some embodiments, thethickness of electrically conductive layers 22 and 23 is between about500 nm and about 100 nm. In other embodiments, the electricallyconductive layers 22 and 23 each have a thickness that is between about400 nm and about 200 nm. In general, thicker or thinner layers may beemployed so long as they provide the necessary electrical properties(e.g., conductivity) and optical properties (e.g., transmittance). Forcertain applications it will generally be preferred that electricallyconductive layers 22 and 23 be as thin as possible to increasetransparency and to reduce cost.

Referring again to FIG. 1, the function of the electrically conductivelayers is to apply the electric potential provided by a power supplyover the entire surface of the electrochromic stack 28 to interiorregions of the stack. The electric potential is transferred to theconductive layers though electrical connections to the conductivelayers. In some embodiments, bus bars, one in contact with firstelectrically conductive layer 22 and one in contact with secondelectrically conductive layer 23 provide the electric connection betweenthe voltage source and the electrically conductive layers 22 and 23.

In one embodiment, the sheet resistance, R₉, of the first and secondelectrically conductive layers 22 and 23 is about 500Ω/□ to 1Ω/□. Insome embodiments, the sheet resistance of first and second electricallyconductive layers 22 and 23 is about 100Ω/□ to 5Ω/□. In general, it isdesirable that the sheet resistance of each of the first and secondelectrically conductive layers 22 and 23 be about the same. In oneembodiment, first and second electrically conductive layers 22 and 23each have a sheet resistance of about 20Ω/□ to about 8Ω/□.

To facilitate more rapid switching of electrochromic device 1 from astate of relatively greater transmittance to a state of relativelylesser transmittance, or vice versa, at least one of electricallyconductive layers 22, 23 preferably has a sheet resistance, R_(s), tothe flow of electrons through the layer that is non-uniform. Forexample, in one embodiment only one of first and second electricallyconductive layers 22, 23 has a non-uniform sheet resistance to the flowof electrons through the layer. Alternatively, and typically morepreferably, first electrically conductive layer 22 and secondelectrically conductive layer 23 each have a non-uniform sheetresistance to the flow of electrons through the respective layers.Without being bound by any particular theory, it is presently believedthat spatially varying the sheet resistance of electrically conductivelayer 22, spatially varying the sheet resistance of electricallyconductive layer 23, or spatially varying the sheet resistance ofelectrically conductive layer 22 and electrically conductive layer 23improves the switching performance of the device by controlling thevoltage drop in the conductive layer to provide uniform potential dropor a desired non-uniform potential drop across the device, over the areaof the device.

In general, electrical circuit modeling may be used to determine thesheet resistance distribution providing desired switching performance,taking into account the type of electrochromic device, the device shapeand dimensions, electrode characteristics, and the placement ofelectrical connections (e.g., bus bars) to the voltage source. The sheetresistance distribution, in turn, can be controlled, at least in part,by grading the thickness of the first and/or second electricallyconductive layer(s), grading the composition of the first and/or secondelectrically conductive layer(s), or patterning the first and/or secondelectrically conductive layer(s), or some combination of these.

In one exemplary embodiment, the electrochromic device is a rectangularelectrochromic window. Referring again to FIG. 1, in this embodimentfirst substrate 24 and second substrate 25 are rectangular panes ofglass or other transparent substrate and electrochromic device 1 has twobus bars 26, 27 located on opposite sides of first electrode layer 20and second electrode layer 21, respectively. When configured in thismanner, it is generally preferred that the resistance to the flow ofelectrons in first electrically conductive layer 22 increases withincreasing distance from bus bar 26 and that the resistance to the flowof electrons in second electrically conductive layer 23 increases withincreasing distance from bus bar 27. This, in turn, can be effected, forexample, by decreasing the thickness of first electrically conductivelayer 22 as a function of increasing distance from bus bar 26 anddecreasing the thickness of second electrically conductive layer 23 as afunction of increasing distance from bus bar 27.

The multi-layer devices of the present invention may have a shape otherthan rectangular, may have more than two bus bars, and/or may not havethe bus bars on opposite sides of the device. For example, themulti-layer device may have a perimeter that is more generally aquadrilateral, or a shape with greater or fewer sides than four forexample, the multi-layer device may be triangular, pentagonal,hexagonal, etc., in shape. By way of further example, the multi-layerdevice may have a perimeter that is curved but lacks vertices, e.g.,circular, oval, etc. By way of further example, the multi-layer devicemay comprise three, four or more bus bars connecting the multi-layerdevice to a voltage source, or the bus bars, independent of number maybe located on non-opposing sides. In each of such instances, thepreferred resistance profile in the electrically conductive layer(s) mayvary from that which is described for the rectangular, two bus barconfiguration.

In general, however, and independent of whether the multi-layer devicehas a shape other than rectangular, there are more than two electricalconnections (e.g., bus bars), and/or the electrical connections (e.g.,bus bars) are on opposite sides of the device, the sheet resistance,R_(s), in the first electrically conductive layer 22, in the secondelectrically conductive layer 23, or in the first electricallyconductive layer 22 and the second electrically conductive layer 23 maybe plotted to join points of equal sheet resistance (i.e., isoresistancelines) as a function of (two-dimensional) position within the firstand/or second electrically conductive layer. Plots of this generalnature, sometimes referred to as contour maps, are routinely used incartography to join points of equal elevation. In the context of thepresent invention, a contour map of the sheet resistance, R_(s), in thefirst and/or second electrically conductive layer as a function of(two-dimensional) position within the first and/or second electricallyconductive layer preferably contains a series of isoresistance lines(also sometimes referred to as contour lines) and resistance gradientlines (lines perpendicular to the isoresistance lines). The sheetresistance along a gradient line in the first and/or second electricallyconductive layer(s) generally increase(s), generally decrease(s),generally increase(s) until it reaches a maximum and then generallydecrease(s), or generally decrease(s) until it reaches a minimum andthen generally increase(s).

FIGS. 2A-2E depict a contour map of the sheet resistance, R_(s), in anelectrically conductive layer (i.e., the first electrically conductivelayer, the second electrically conductive layer, or each of the firstand second electrically conductive layers) as a function of(two-dimensional) position within the electrically conductive layer forseveral exemplary embodiments of an electrochromic stack in accordancewith the present invention. In each of FIGS. 2A-2E, contour map 50depicts a set of sheet isoresistance curves 52 (i.e., curves along whichthe sheet resistance, R₈, has a constant value) and a set of resistancegradient curves 54 that are perpendicular to isoresistance curves 52resulting from an electrochromic stack having a perimeter that is square(FIGS. 2A, 2B, and 2C) or circular (FIGS. 2D and 2E) and varying numbersand locations of bus bars 226 and 227 in contact with the first andsecond electrically conductive layers (not labeled) of theelectrochromic stack. In FIG. 2A, the direction of the set of gradients54 indicates that the sheet resistance, R_(s), within the electricallyconductive layer progressively increases along the set of gradients 54and between west side 55 and east side 56 of the electrically conductivelayer in contact with bus bar 227. In FIG. 2B, the direction of gradient54A indicates that the sheet resistance, R_(s), within the electricallyconductive layer in contact with bus bar 227 progressively decreasesfrom southwest corner 57 to centroid 59 and then decreases from centroid59 to northeast corner 58. In FIG. 2C, the direction of the set ofgradients 54 indicate that the sheet resistance, R_(s), within theelectrically conductive layer in contact with bus bar 227 progressivelydecreases from the west side 60 and east side 61 to centroid 59 andprogressively increases from the top side 58 and bottom side 57 tocentroid 59; stated differently, sheet resistance, R_(s), forms a saddlelike form centered around centroid 59. In FIG. 2D, the direction ofgradients 54 a and 54 b indicates that the sheet resistance, R_(s),within the electrically conductive layer in contact with bus bar 227progressively decreases from each of positions 64 and 65 to centroid 59and progressively increases from each of positions 63 and 62 to centroid59; stated differently, sheet resistance, R_(s), forms a saddle likeform centered around centroid 59. In FIG. 2E, the direction of the setof gradients 54 indicates that the sheet resistance, R_(s), within theelectrically conductive layer in contact with bus bar 227 progressivelydecreases from the west side 55 to the east side 56. In one embodiment,for example, the gradient in sheet resistance is a constant. By way offurther example, in one embodiment, the gradient in sheet resistance isa constant and the substrate is rectangular in shape

In one presently preferred embodiment, the ratio of the value of maximumsheet resistance, R_(max), to the value of minimum sheet resistance,R_(min), in the first electrically conductive layer is at least about1.25. In one exemplary embodiment, the ratio of the value of maximumsheet resistance, R_(max), to the value of minimum sheet resistance,R_(max), in the first electrically conductive layer is at least about1.5. In one exemplary embodiment, the ratio of the value of maximumsheet resistance, R_(max), to the value of minimum sheet resistance,R_(min), in the first electrically conductive layer is at least about 2.In one exemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 3. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 4. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 5. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 6. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 7. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 8. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 9. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first electrically conductive layer is at least about 10.

FIG. 21 illustrates the non-uniformity in the sheet resistance of firstelectrically conductive layer 22 of multi-layer electrochromic device 1.First electrically conductive layer 22 comprises a sheet resistancegradient curve (the line comprising line segment X₁-Y₁, indicating thatthe sheet resistance, R_(s), within electrically conductive layer 22progressively increases as described in connection with FIG. 2). BetweenX₁ and Y₁, the sheet resistance of first electrically conductive layer22 generally increases, generally decreases or generally increases andthen decreases. In one embodiment, line segment X₁-Y₁ has a length of atleast 1 cm. For example, line segment X₁-Y₁ may have a length of 2.5 cm,5 cm, 10 cm, or 25 cm. Additionally, line segment X₁-Y₁ may be straightor curved.

In one embodiment, the non-uniformity in the sheet resistance of thefirst electrically conductive layer may be observed by comparing theratio of the average sheet resistance, R_(avg) in two different regionsof the first electrically conductive layer wherein the first and secondregions are each circumscribed by a convex polygon and each comprises atleast 25% of the surface area of the first electrically conductivelayer. For example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 1.25wherein each of the first and second regions is circumscribed by aconvex polygon, and each comprises at least 25% of the surface area ofthe first electrically conductive layer. This may be illustrated byreference to FIG. 21. First electrically conductive layer 22 comprisesconvex polygon A₁ and convex polygon B₁ and each circumscribes a regioncomprising at least 25% of the surface area of first electricallyconductive layer 22; in one embodiment, the ratio of the average sheetresistance, R¹ _(avg), in a first region of the first electricallyconductive layer bounded by convex polygon A₁ to the average sheetresistance, R² _(avg), in a second region of the first electricallyconductive layer bounded by convex polygon B₁ is at least 1.25. Asillustrated, convex polygon A₁ is a triangle and convex polygon B₁ is asquare merely for purposes of exemplification; in practice, the firstregion may be bounded by any convex polygon and the second region may bebounded by any convex polygon. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 1.5 wherein the first and second regionsare each circumscribed by a convex polygon and each comprises at least25% of the surface area of the first electrically conductive layer. Byway of further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 2wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of the firstelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 3 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the first electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 4wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of the firstelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 5 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the first electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 6wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of the firstelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 7 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the first electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 8wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of the firstelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 9 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the first electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 10wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of the firstelectrically conductive layer. In one embodiment in each of theforegoing examples, the first and second regions are mutually exclusiveregions.

In one embodiment, the non-uniformity in the sheet resistance of thefirst electrically conductive layer may be observed by comparing theaverage sheet resistance, R_(avg) in four different regions of the firstelectrically conductive layer wherein the first region is contiguouswith the second region, the second region is contiguous with the thirdregion, the third region is contiguous with the fourth region, each ofthe regions is circumscribed by a convex polygon, and each comprises atleast 10% of the surface area of the first electrically conductivelayer. For example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the first electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe first electrically conductive layer, R² _(avg), is at least 1.25,the ratio of the average sheet resistance in the second region of thefirst electrically conductive layer, R² _(avg), to the average sheetresistance in a third region of the first electrically conductive layer,R³ _(avg), is at least 1.25, the ratio of the average sheet resistancein the third region of the first electrically conductive layer, R³_(avg), to the average sheet resistance in a fourth region of the firstelectrically conductive layer, R⁴ _(avg), is at least 1.25, wherein thefirst region is contiguous with the second region, the second region iscontiguous with the third region, the third region is contiguous withthe fourth region, each of the regions is circumscribed by a convexpolygon, and each comprises at least 10% of the surface area of thefirst electrically conductive layer. By way of further example, in onesuch embodiment, the ratio of the average sheet resistance in a firstregion of the first electrically conductive layer, R¹ _(avg), to theaverage sheet resistance in a second region of the first electricallyconductive layer, R² _(avg), is at least 1.5, the ratio of the averagesheet resistance in the second region of the first electricallyconductive layer, R² _(avg), to the average sheet resistance in a thirdregion of the first electrically conductive layer, R³ _(avg), is atleast 1.5, the ratio of the average sheet resistance in the third regionof the first electrically conductive layer, R³ _(avg), to the averagesheet resistance in a fourth region of the first electrically conductivelayer, R⁴ _(avg), is at least 1.5, wherein the first region iscontiguous with the second region, the second region is contiguous withthe third region, the third region is contiguous with the fourth region,each of the regions is circumscribed by a convex polygon, and eachcomprises at least 10% of the surface area of the first electricallyconductive layer. By way of further example, in one such embodiment, theratio of the average sheet resistance in a first region of the firstelectrically conductive layer, R¹ _(avg), to the average sheetresistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 2, the ratio of the average sheetresistance in the second region of the first electrically conductivelayer, R² _(avg), to the average sheet resistance in a third region ofthe first electrically conductive layer, R³ _(avg), is at least 2, theratio of the average sheet resistance in the third region of the firstelectrically conductive layer, R³ _(avg), to the average sheetresistance in a fourth region of the first electrically conductivelayer, R⁴ _(avg), is at least 2, wherein the first region is contiguouswith the second region, the second region is contiguous with the thirdregion, the third region is contiguous with the fourth region, each ofthe regions is circumscribed by a convex polygon, and each comprises atleast 10% of the surface area of the first electrically conductivelayer. In one embodiment in each of the foregoing examples, the first,second, third and fourth regions are mutually exclusive regions.

In one presently preferred embodiment, the second electricallyconductive layer has a sheet resistance, R_(s), to the flow ofelectrical current through the second electrically conductive layer thatvaries as a function of position in the second electrically conductivelayer. In one such embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 1.25. Inone exemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 1.5. Inone exemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 2. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 3. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 4. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 5. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 6. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 7. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 8. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 9. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the second electrically conductive layer is at least about 10.

FIG. 21 illustrates the non-uniformity in the sheet resistance of secondelectrically conductive layer 23 of multi-layer electrochromic device 1.Electrically conductive layer 22 comprises sheet resistance gradientcurve 54 which includes line segment X-Y; between X and Y, the sheetresistance of second electrically conductive layer 23 generallyincreases, generally decreases or generally increases and thendecreases. In one embodiment, line segment X₁-Y₁ has a length of atleast 1 cm. For example, line segment X-Y may have a length of 2.5 cm, 5cm, 10 cm, or 25 cm. Additionally, line segment X-Y may be straight orcurved.

In one embodiment, the non-uniformity in the sheet resistance of thesecond electrically conductive layer may be observed by comparing theratio of the average sheet resistance, R_(avg) in two different regionsof the second electrically conductive layer wherein the first and secondregions are each circumscribed by a convex polygon and each comprises atleast 25% of the surface area of the second electrically conductivelayer. For example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 1.25wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of thesecond electrically conductive layer. This may be illustrated byreference to FIG. 21. Second electrically conductive layer 23 comprisesconvex polygon A and convex polygon B and each circumscribes a regioncomprising at least 25% of the surface area of second electricallyconductive layer 23; in one embodiment, the ratio of the average sheetresistance, R¹ _(avg), in a first region of the second electricallyconductive layer bounded by convex polygon A to the average sheetresistance, R² _(avg), in a second region of the second electricallyconductive layer bounded by convex polygon B is at least 1.25. Asillustrated, convex polygon A is a triangle and convex polygon B is asquare merely for purposes of exemplification; in practice, the firstregion may be bounded by any convex polygon and the second region may bebounded by any convex polygon. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the second electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the second electricallyconductive layer, R² _(avg), is at least 1.5 wherein the first andsecond regions are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the second electricallyconductive layer. By way of further example, in one such embodiment, theratio of the average sheet resistance in a first region of the secondelectrically conductive layer, R¹ _(avg), to the average sheetresistance in a second region of the second electrically conductivelayer, R² _(avg), is at least 2 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the second electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 3wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of thesecond electrically conductive layer. By way of further example, in onesuch embodiment, the ratio of the average sheet resistance in a firstregion of the second electrically conductive layer, R¹ _(avg), to theaverage sheet resistance in a second region of the second electricallyconductive layer, R² _(avg), is at least 4 wherein the first and secondregions are each circumscribed by a convex polygon and each comprises atleast 25% of the surface area of the second electrically conductivelayer. By way of further example, in one such embodiment, the ratio ofthe average sheet resistance in a first region of the secondelectrically conductive layer, R¹ _(avg), to the average sheetresistance in a second region of the second electrically conductivelayer, R² _(avg), is at least 5 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the second electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 6wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of thesecond electrically conductive layer. By way of further example, in onesuch embodiment, the ratio of the average sheet resistance in a firstregion of the second electrically conductive layer, R¹ _(avg), to theaverage sheet resistance in a second region of the second electricallyconductive layer, R² _(avg), is at least 7 wherein the first and secondregions are each circumscribed by a convex polygon and each comprises atleast 25% of the surface area of the second electrically conductivelayer. By way of further example, in one such embodiment, the ratio ofthe average sheet resistance in a first region of the secondelectrically conductive layer, R¹ _(avg), to the average sheetresistance in a second region of the second electrically conductivelayer, R² _(avg), is at least 8 wherein the first and second regions areeach circumscribed by a convex polygon and each comprises at least 25%of the surface area of the second electrically conductive layer. By wayof further example, in one such embodiment, the ratio of the averagesheet resistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 9wherein the first and second regions are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of thesecond electrically conductive layer. By way of further example, in onesuch embodiment, the ratio of the average sheet resistance in a firstregion of the second electrically conductive layer, R¹ _(avg), to theaverage sheet resistance in a second region of the second electricallyconductive layer, R² _(avg), is at least 10 wherein the first and secondregions are each circumscribed by a convex polygon and each comprises atleast 25% of the surface area of the second electrically conductivelayer. In one embodiment in each of the foregoing examples, the firstand second regions are mutually exclusive regions.

In one embodiment, the non-uniformity in the sheet resistance of thesecond electrically conductive layer may be observed by comparing theaverage sheet resistance, R_(avg) in four different regions of thesecond electrically conductive layer wherein the first region iscontiguous with the second region, the second region is contiguous withthe third region, the third region is contiguous with the fourth region,each of the regions is circumscribed by a convex polygon, and eachcomprises at least 10% of the surface area of the second electricallyconductive layer. For example, in one such embodiment, the ratio of theaverage sheet resistance in a first region of the second electricallyconductive layer, R¹ _(avg), to the average sheet resistance in a secondregion of the second electrically conductive layer, R² _(avg), is atleast 1.25, the ratio of the average sheet resistance in the secondregion of the second electrically conductive layer, R² _(avg), to theaverage sheet resistance in a third region of the second electricallyconductive layer, R³ _(avg), is at least 1.25, the ratio of the averagesheet resistance in the third region of the second electricallyconductive layer, R³ _(avg), to the average sheet resistance in a fourthregion of the second electrically conductive layer, R⁴ _(avg), is atleast 1.25, wherein the first region is contiguous with the secondregion, the second region is contiguous with the third region, the thirdregion is contiguous with the fourth region, each of the regions iscircumscribed by a convex polygon, and each comprises at least 10% ofthe surface area of the second electrically conductive layer. By way offurther example, in one such embodiment, the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 1.5,the ratio of the average sheet resistance in the second region of thesecond electrically conductive layer, R² _(avg), to the average sheetresistance in a third region of the second electrically conductivelayer, R³ _(avg), is at least 1.5, the ratio of the average sheetresistance in the third region of the second electrically conductivelayer, R³ _(avg), to the average sheet resistance in a fourth region ofthe second electrically conductive layer, R⁴ _(avg), is at least 1.5,wherein the first region is contiguous with the second region, thesecond region is contiguous with the third region, the third region iscontiguous with the fourth region, each of the regions is circumscribedby a convex polygon, and each comprises at least 10% of the surface areaof the second electrically conductive layer. By way of further example,in one such embodiment, the ratio of the average sheet resistance in afirst region of the second electrically conductive layer, R¹ _(avg), tothe average sheet resistance in a second region of the secondelectrically conductive layer, R² _(avg), is at least 2, the ratio ofthe average sheet resistance in the second region of the secondelectrically conductive layer, R² _(avg), to the average sheetresistance in a third region of the second electrically conductivelayer, R³ _(avg), is at least 2, the ratio of the average sheetresistance in the third region of the second electrically conductivelayer, R³ _(avg), to the average sheet resistance in a fourth region ofthe second electrically conductive layer, R⁴ _(avg), is at least 2,wherein the first region is contiguous with the second region, thesecond region is contiguous with the third region, the third region iscontiguous with the fourth region, each of the regions is circumscribedby a convex polygon, and each comprises at least 10% of the surface areaof the second electrically conductive layer. In one embodiment in eachof the foregoing examples, the first, second, third and fourth regionsare mutually exclusive regions.

In one presently preferred embodiment, first and second electricallyconductive layers 22, 23 have a sheet resistance, R_(s), to the flow ofelectrical current through the second electrically conductive layer thatvaries as a function of position in the first and second electricallyconductive layers. Although it is generally preferred in this embodimentthat the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in the first and secondelectrically conductive layers be approximately the same, they may havedifferent values. For example, in one such embodiment, the ratio of thevalue of maximum sheet resistance, R_(max), to the value of minimumsheet resistance, R_(min), in the first electrically conductive layerhas a value that is at least twice as much as the ratio of the value ofmaximum sheet resistance, R_(max), to the value of minimum sheetresistance, R_(min), in the second electrically conductive layer. Moretypically, however, the ratio of the value of maximum sheet resistance,R_(max), to the value of minimum sheet resistance, R_(min), in the firstand second electrically conductive layers will be approximately the sameand each at least about 1.25. In one exemplary embodiment, the ratio ofthe value of maximum sheet resistance, R_(max), to the value of minimumsheet resistance, R_(min), the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),in the first and second electrically conductive layers will beapproximately the same and each at least about 1.5. In one exemplaryembodiment, the ratio of the value of maximum sheet resistance, R_(max),to the value of minimum sheet resistance, R_(min), the ratio of thevalue of maximum sheet resistance, R_(max), to the value of minimumsheet resistance, R_(min), in each of the first and second electricallyconductive layers is at least about 2. In one exemplary embodiment, theratio of the value of maximum sheet resistance, R_(max), to the value ofminimum sheet resistance, R_(min), the ratio of the value of maximumsheet resistance, R_(max), to the value of minimum sheet resistance,R_(min), in each of the first and second electrically conductive layersis at least about 3. In one exemplary embodiment, the ratio of the valueof maximum sheet resistance, R_(max), to the value of minimum sheetresistance, R_(min), the ratio of the value of maximum sheet resistance,R_(max), to the value of minimum sheet resistance, R_(min), in each ofthe first and second electrically conductive layers is at least about 4.In one exemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 5. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 6. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 7. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 8. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 9. In oneexemplary embodiment, the ratio of the value of maximum sheetresistance, R_(max), to the value of minimum sheet resistance, R_(min),the ratio of the value of maximum sheet resistance, R_(max), to thevalue of minimum sheet resistance, R_(min), in each of the first andsecond electrically conductive layers is at least about 10.

In one embodiment, the non-uniformity in the sheet resistance of thefirst and second electrically conductive layers may be observed bycomparing the ratio of the average sheet resistance, R_(avg) in twodifferent regions of the first and second electrically conductivelayers, respectively, wherein the first and second regions of the firstelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the firstelectrically conductive layer and the first and second regions of thesecond electrically conductive layer are each circumscribed by a convexpolygon and each comprises at least 25% of the surface area of thesecond electrically conductive layer. For example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 1.25 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 1.25wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 1.5 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 1.5wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 2 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 2wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 3 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 3wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 4 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 4wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 5 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 5wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 6 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 6wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 7 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 7wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 8 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 8wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 9 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 9wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. By way of further example, in one suchembodiment, the ratio of the average sheet resistance in a first regionof the first electrically conductive layer, R¹ _(avg), to the averagesheet resistance in a second region of the first electrically conductivelayer, R² _(avg), is at least 10 and the ratio of the average sheetresistance in a first region of the second electrically conductivelayer, R¹ _(avg), to the average sheet resistance in a second region ofthe second electrically conductive layer, R² _(avg), is at least 10wherein the first and second regions of the first electricallyconductive layer are each circumscribed by a convex polygon and eachcomprises at least 25% of the surface area of the first electricallyconductive layer and the first and second regions of the secondelectrically conductive layer are each circumscribed by a convex polygonand each comprises at least 25% of the surface area of the secondelectrically conductive layer. In one embodiment in each of theforegoing examples, the first and second regions are mutually exclusiveregions.

Referring again to FIG. 21, the spatial non-uniformity of the sheetresistance of the first and second electrically conductive layer may becorrelated in accordance with one aspect of the present invention. Forexample, line segment X₁-Y₁ in first electrically conductive layer 22may be projected through second electrode layer 21, ion conductor layer10 and first electrode layer 20 and onto second electrically conductivelayer 23, with the projection defining line segment X-Y. In general, ifthe sheet resistance generally increases in first electricallyconductive layer 22 along line segment X₁-Y₁ (i.e., the sheet resistancegenerally increases moving along the sheet resistance gradient curve inthe direction from point X₁ to point Y₁), the sheet resistance generallydecreases in second electrically conductive layer 23 along segment X-Y(i.e., the sheet resistance generally decreases along sheet resistancegradient curve 54 and in the direction from point X to point Y). Aspreviously noted, line segments X-Y and X₁-Y₁ have a length of at least1 cm. For example, line segments X-Y and X₁-Y₁ may have a length of 2.5cm, 5 cm, 10 cm, or 25 cm. Additionally, line segments X-Y and X₁-Y₁ maybe straight or curved. In one embodiment, for example, the sheetresistance gradients in electrically conductive layers 22, 23 arenon-zero constants and are of opposite sign (e.g., the sheet resistancegenerally increases linearly in first electrically conductive layeralong in the direction from point X₁ to point Y₁ and generally decreaseslinearly along sheet resistance gradient curve 54 in the direction frompoint X to point Y). By way of further example, in one embodiment,substrates 24, 25 are rectangular and the sheet resistance gradients inelectrically conductive layers 22, 23 are non-zero constants and are ofopposite sign (e.g., the sheet resistance generally increases linearlyin second electrically conductive layer 23 along gradient 54 in thedirection from point X to point Y and generally decreases linearly infirst electrically conductive layer 22 along the line containing linesegment X₁-Y₁ in the direction from point X₁ to point Y₁).

In another embodiment, and still referring to FIG. 21, the spatialnon-uniformity of the sheet resistance of the first and secondelectrically conductive layers may be characterized by reference toseparate first and second regions in the first electrically conductivelayer and their projections onto the second electrically conductivelayer to define complementary first and second regions in the secondelectrically conductive layer wherein the first and second regions ofthe first electrically conductive layer are each bounded by a convexpolygon, each contain at least 25% of the surface area of the firstelectrically conductive layer, and are mutually exclusive regions. Ingeneral, the first electrically conductive layer has an average sheetresistance in the first and regions of the first electrically conductivelayer and the second electrically conductive layer has an average sheetresistance in the complementary first and second regions of the secondelectrically conductive layer wherein: (a) (i) a ratio of the averagesheet resistance of the first electrically conductive layer in the firstregion to the average sheet resistance of the first electricallyconductive layer in the second region is at least 1.5 or (ii) a ratio ofthe average sheet resistance of the second electrically conductive layerin the complementary first region to the average sheet resistance of thesecond electrically conductive layer in the complementary second regionis greater than 1.5 and (b) a ratio of the average sheet resistance ofthe first electrically conductive layer in the first region to theaverage sheet resistance of the second electrically layer in thecomplementary first region (i.e., the projection of the first region ofthe first electrically conductive layer onto the second electricallyconductive layer) is at least 150% of the ratio of the average sheetresistance of the first electrically conductive layer in the secondregion to the average sheet resistance of the second electrically layerin the complementary second region (i.e., the projection of the secondregion of the first electrically conductive layer onto the secondelectrically conductive layer).

Referring again to FIG. 21, first electrically conductive layer 22comprises a region A₁ and a region B₁ wherein region A₁ and region B₁each comprise at least 25% of the surface area of the first electricallyconductive layer, are each circumscribed by a convex polygon and aremutually exclusive regions. A projection of region A₁ onto secondelectrically conductive layer 23 defines a region A circumscribed by aconvex polygon in the second electrically conductive layer comprising atleast 25% of the surface area of the second electrically conductivelayer. A projection of region B₁ onto the second electrically conductivelayer defines a region B circumscribed by a convex polygon in the secondelectrically conductive layer comprising at least 25% of the surfacearea of the second electrically conductive layer. First electricallyconductive layer 22 has an average sheet resistance in region A₁corresponding to R^(A1) _(avg) and an average sheet resistance in regionB₁ corresponding to R^(B1) _(avg). Second electrically conductive layer23 has an average sheet resistance in region A corresponding to R^(A)_(avg) and an average sheet resistance in region B corresponding toR^(B) _(avg). In accordance with one embodiment, (i) the ratio of R^(A1)_(avg) to R^(B1) _(avg) or the ratio of R^(B) _(avg) to R^(A) _(avg) isat least 1.5 and (ii) the ratio of (R^(A1) _(avg)/R^(A) _(avg)) to(R^(B1) _(avg)/R^(B) _(avg)) is at least 1.5. For example, in oneembodiment, (i) the ratio of R^(A1) _(avg) to R^(B1) _(avg) or the ratioof R^(B) _(avg) to R^(A) _(avg) is at least 1.75 and (ii) the ratio of(R^(A1) _(avg)/R^(A) _(avg)) to (R^(B1) _(avg)/R^(B) _(avg)) is at least1.75. By way of further example, in one embodiment, (i) the ratio ofR^(A1) _(avg) to R^(B1) _(avg) or the ratio of R^(B) _(avg), to R^(A)_(avg) is at least 2 and (ii) the ratio of (R^(A1) _(avg)/R^(A) _(avg))to (R^(B1) _(avg)/R^(B) _(avg)) is at least 2. By way of furtherexample, in one embodiment, (i) the ratio of R^(A1) _(avg) to R^(B1)_(avg) or the ratio of R^(B) _(avg) to R^(A) _(avg) is at least 3 and(ii) the ratio of (R^(A1) _(avg)/R^(A) _(avg)) to (R^(B1) _(avg)/R^(B)_(avg)) is at least 3. By way of further example, in one embodiment, (i)the ratio of R^(A1) _(avg) to R^(B1) _(avg) or the ratio of R^(B) _(avg)to R^(A) _(avg) is at least 5 and (ii) the ratio of (R^(A1) _(avg)/R^(A)_(avg)) to (R^(B1) _(avg)/R^(B) _(avg)) is at least 5. By way of furtherexample, in one embodiment, (i) the ratio of R^(A1) _(avg) to R^(B1)_(avg) or the ratio of R^(B) _(avg) to R^(A) _(avg) is at least 10 and(ii) the ratio of (R^(A1) _(avg)/R^(A) _(avg)) to (R^(B1) _(avg)/R^(B)_(avg)) is at least 10.

Without wishing to be bound by any particular theory, and based uponcertain experimental evidence obtained to-date, in certain embodimentsthe electrode sheet resistance may be expressed as a function ofposition in a large area electrochromic device that provides a localvoltage drop across the electrochromic stack that is substantiallyconstant. For the simple geometry shown in FIG. 1, where the contact(bus bar 27) to the top electrode is made at x=0 and the contact (busbar 26) to the bottom electrode is made at x=xt, the relationship issimply that

R′(x)=R(x)*(xt/x−1);

where R(x) is the sheet resistance of the top electrode as a function ofposition and R′(x) is the sheet resistance of the bottom electrode as afunction of position. A simple mathematical example of this relationshipis that for a linear change in the sheet resistance of the topelectrode, R(x)=a*x, the sheet resistance of the bottom electrode mustbe R′(x)=a*(xt−x). Another simple example is that for R(x)=1/(xt−a*x)then R′(x)=1/(a*x). This relationship holds in a mathematical sense forany function R(x). This relationship can be generalized to any electrodesheet resistance distribution that smoothly varies and any contactconfiguration by the following relationship between the sheet resistancefrom one contact (z=0) to anther (z=L) along gradient curves that areperpendicular to iso-resistance lines R(z), and the correspondingopposing electrode sheet resistance distribution R′(z).

R′(z)=R(z)*(L/z−1);

As a practical matter, devices do not need to precisely adhere to thisrelationship to realize the benefits of this invention. For example, inthe case above where R′(x)=1/(a*x), R′(0)=infinity. While one canpractically create resistances of very large magnitude, a film with aR′(x)=1/(a*x+b) where b is small relative to a can exhibit significantlyimproved switching uniformity over a device comprising electrodes ofuniform sheet resistance.

Electrically conductive layers having a non-uniform sheet resistance maybe prepared by a range of methods. In one embodiment, the non-uniformsheet resistance is the result of a composition variation in the layer;composition variations may be formed, for example, by sputter coatingfrom two cylindrical targets of different materials while varying thepower to each target as a function of position relative to thesubstrate, by reactive sputter coating from a cylindrical target whilevarying the gas partial pressure and/or composition as a function ofposition relative to the substrate, by spray coating with a varyingcomposition or process as a function of position relative to thesubstrate, or by introducing a dopant variation to a uniform compositionand thickness film by ion implantation, diffusion, or reaction. Inanother embodiment, the non-uniform sheet resistance is the result of athickness variation in the layer; thickness variations may be formed,for example, by sputter coating from a cylindrical target while varyingthe power to the target as a function of as a function of positionrelative to the substrate, sputter coating from a target at constantpower and varying the velocity of substrate under the target as afunction of as a function of position relative to the substrate, adeposited stack of uniform TCO films 222 a-222 r on substrate 224 whereeach film has a limited spatial extent as illustrated in FIG. 3.Alternatively, a thickness gradient can be formed by starting with auniform thickness conductive layer and then etching the layer in a waythat is spatially non-uniform such as dip-etching or spraying withetchant at a non-uniform rate across the layer. In another embodiment,the non-uniform sheet resistance is the result of patterning; gradientsmay be introduced, for example, by laser patterning a series of scribesinto a constant thickness and constant resistivity film to create adesired spatially varying resistivity. In addition to laser patterning,mechanical scribing and lithographic patterning using photoresists (asknown in the art of semiconductor device manufacturing) can be used tocreate a desired spatially varying resistivity. In another embodiment,the non-uniform sheet resistance is the result of a defect variation; adefect variation may be introduced, for example, by introducingspatially varying defects via ion implantation, or creating a spatiallyvarying defect density via a spatially varying annealing process appliedto a layer with a previously uniform defect density.

Referring again to FIG. 1, at least one of first and second electrodelayers 20 and 21 is electrochromic, one of the first and secondelectrode layers is the counter electrode for the other, and first andsecond electrode layers 20 and 21 are inorganic and/or solid.Non-exclusive examples of electrochromic electrode layers 20 and 21 arecathodically coloring thin films of oxides based on tungsten,molybdenum, niobium, titanium, lead and/or bismuth, or anodicallycoloring thin films of oxides, hydroxides and/or oxy-hydrides based onnickel, iridium, iron, chromium, cobalt and/or rhodium.

In one embodiment, first electrode layer 20 contains any one or more ofa number of different electrochromic materials, including metal oxides.Such metal oxides include tungsten oxide (WO₃), molybdenum oxide (MoO₃),niobium oxide (Nb₂O₅), titanium oxide (TiO₂), copper oxide (CuO),iridium oxide (Ir₂O₃), chromium oxide (Cr₂O₃), manganese oxide (Mn₂O₃),vanadium oxide (V₂O₃), nickel oxide (Ni₂O₃), cobalt oxide (Co₂O₃) andthe like. In some embodiments, the metal oxide is doped with one or moredopants such as lithium, sodium, potassium, molybdenum, vanadium,titanium, and/or other suitable metals or compounds containing metals.Mixed oxides (e.g., W—Mo oxide, W—V oxide) are also used in certainembodiments.

In some embodiments, tungsten oxide or doped tungsten oxide is used forfirst electrode layer 20. In one embodiment, first electrode layer 20 iselectrochromic and is made substantially of WO_(x), where “x” refers toan atomic ratio of oxygen to tungsten in the electrochromic layer, and xis between about 2.7 and 3.5. It has been suggested that onlysub-stoichiometric tungsten oxide exhibits electrochromism; i.e.,stoichiometric tungsten oxide, WO₃, does not exhibit electrochromism. Ina more specific embodiment, WO_(x), where x is less than 3.0 and atleast about 2.7 is used for first electrode layer 20. In anotherembodiment, first electrode layer 20 is WO_(x), where x is between about2.7 and about 2.9. Techniques such as Rutherford BackscatteringSpectroscopy (RBS) can identify the total number of oxygen atoms whichinclude those bonded to tungsten and those not bonded to tungsten. Insome instances, tungsten oxide layers where x is 3 or greater exhibitelectrochromism, presumably due to unbound excess oxygen along withsub-stoichiometric tungsten oxide. In another embodiment, the tungstenoxide layer has stoichiometric or greater oxygen, where x is 3.0 toabout 3.5.

In certain embodiments, the electrochromic mixed metal oxide iscrystalline, nanocrystalline, or amorphous. In some embodiments, thetungsten oxide is substantially nanocrystalline, with grain sizes, onaverage, from about 5 nm to 50 nm (or from about 5 nm to 20 nm), ascharacterized by transmission electron microscopy (TEM). The tungstenoxide morphology may also be characterized as nanocrystalline usingx-ray diffraction (XRD); XRD. For example, nanocrystallineelectrochromic tungsten oxide may be characterized by the following XRDfeatures: a crystal size of about 10 to 100 nm (e.g., about 55 nm.Further, nanocrystalline tungsten oxide may exhibit limited long rangeorder, e.g., on the order of several (about 5 to 20) tungsten oxide unitcells.

The thickness of the first electrode layer 20 depends on theelectrochromic material selected for the electrochromic layer. In someembodiments, first electrode layer 20 is about 50 nm to 2,000 nm, orabout 100 nm to 700 nm. In some embodiments, the first electrode layer20 is about 250 nm to about 500 nm.

Second electrode layer 21 serves as the counter electrode to firstelectrode layer 20 and, like first electrode layer 20, second electrodelayer 21 may comprise electrochromic materials as well asnon-electrochromic materials. Non-exclusive examples of second electrodelayer 21 are cathodically coloring electrochromic thin films of oxidesbased on tungsten, molybdenum, niobium, titanium, lead and/or bismuth,anodically coloring electrochromic thin films of oxides, hydroxidesand/or oxy-hydrides based on nickel, iridium, iron, chromium, cobaltand/or rhodium, or non-electrochromic thin films, e.g., of oxides basedon vanadium and/or cerium as well as activated carbon. Also combinationsof such materials can be used as second electrode layer 21.

In some embodiments, second electrode layer 21 may comprise one or moreof a number of different materials that are capable of serving asreservoirs of ions when the electrochromic device is in the bleachedstate. During an electrochromic transition initiated by, e.g.,application of an appropriate electric potential, the counter electrodelayer transfers some or all of the ions it holds to the electrochromicfirst electrode layer 20, changing the electrochromic first electrodelayer 20 to the colored state.

In some embodiments, suitable materials for a counter electrodecomplementary to WO₃ include nickel oxide (NiO), nickel tungsten oxide(NiWO), nickel vanadium oxide, nickel chromium oxide, nickel aluminumoxide, nickel manganese oxide, nickel magnesium oxide, chromium oxide(Cr₂O₃), manganese oxide (MnO₂), and Prussian blue. Optically passivecounter electrodes comprise cerium titanium oxide (CeO₂—TiO₂), ceriumzirconium oxide (CeO₂—ZrO₂), nickel oxide (NiO), nickel-tungsten oxide(NiWO), vanadium oxide (V₂O₅), and mixtures of oxides (e.g., a mixtureof Ni₂O₃ and WO₃). Doped formulations of these oxides may also be used,with dopants including, e.g., tantalum and tungsten. Because firstelectrode layer 20 contains the ions used to produce the electrochromicphenomenon in the electrochromic material when the electrochromicmaterial is in the bleached state, the counter electrode preferably hashigh transmittance and a neutral color when it holds significantquantities of these ions.

In some embodiments, nickel-tungsten oxide (NiWO) is used in the counterelectrode layer. In certain embodiments, the amount of nickel present inthe nickel-tungsten oxide can be up to about 90% by weight of thenickel-tungsten oxide. In a specific embodiment, the mass ratio ofnickel to tungsten in the nickel-tungsten oxide is between about 4:6 and6:4 (e.g., about 1:1). In one embodiment, the NiWO is between about 15%(atomic) Ni and about 60% Ni; between about 10% W and about 40% W; andbetween about 30% O and about 75% O. In another embodiment, the NiWO isbetween about 30% (atomic) Ni and about 45% Ni; between about 10% W andabout 25% W; and between about 35% O and about 50% O. In one embodiment,the NiWO is about 42% (atomic) Ni, about 14% W, and about 44% O.

In some embodiments, the thickness of second electrode layer 21 is about50 nm about 650 nm. In some embodiments, the thickness of secondelectrode layer 21 is about 100 nm to about 400 nm, preferably in therange of about 200 nm to 300 nm.

Ion conducting layer 10 serves as a medium through which ions aretransported (in the manner of an electrolyte) when the electrochromicdevice transforms between the bleached state and the colored state. Ionconductor layer 10 comprises an ion conductor material. It may betransparent or non-transparent, colored or non-colored, depending on theapplication. Preferably, ion conducting layer 10 is highly conductive tothe relevant ions for the first and second electrode layers 20 and 21.Depending on the choice of materials, such ions include lithium ions(Li⁺) and hydrogen ions (H⁺) (i.e., protons). Other ions may also beemployed in certain embodiments. These include deuterium ions (D⁺),sodium ions (Na⁺), potassium ions (K⁺), calcium ions (Ca⁺⁺), barium ions(Ba⁺⁺), strontium ions (Sr⁺⁺), and magnesium ions (Mg⁺⁺). Preferably,ion conducting layer 10 also has sufficiently low electron conductivitythat negligible electron transfer takes place during normal operation.In various embodiments, the ion conductor material has an ionicconductivity of between about 10⁻⁵ S/cm and 10⁻³ S/cm.

Some non-exclusive examples of electrolyte types are: solid polymerelectrolytes (SPE), such as poly(ethylene oxide) with a dissolvedlithium salt; gel polymer electrolytes (GPE), such as mixtures ofpoly(methyl methacrylate) and propylene carbonate with a lithium salt;composite gel polymer electrolytes (CGPE) that are similar to GPE's butwith an addition of a second polymer such a poly(ethylene oxide), andliquid electrolytes (LE) such as a solvent mixture of ethylenecarbonate/diethyl carbonate with a lithium salt; and compositeorganic-inorganic electrolytes (CE), comprising an LE with an additionof titania, silica or other oxides. Some non-exclusive examples oflithium salts used are LiTFSI (lithium bis(trifluoromethane)sulfonimide), LiBF₄ (lithium tetrafluoroborate), LiAsF₆ (lithiumhexafluoro arsenate), LiCF₃SO₃ (lithium trifluoromethane sulfonate), andLiClO₄ (lithium perchlorate). Additional examples of suitable ionconducting layers include silicates, silicon oxides, tungsten oxides,tantalum oxides, niobium oxides, and borates. The silicon oxides includesilicon-aluminum-oxide. These materials may be doped with differentdopants, including lithium. Lithium doped silicon oxides include lithiumsilicon-aluminum-oxide. In some embodiments, the ion conducting layercomprises a silicate-based structure. In other embodiments, suitable ionconductors particularly adapted for lithium ion transport include, butare not limited to, lithium silicate, lithium aluminum silicate, lithiumaluminum borate, lithium aluminum fluoride, lithium borate, lithiumnitride, lithium zirconium silicate, lithium niobate, lithiumborosilicate, lithium phosphosilicate, and other such lithium-basedceramic materials, silicas, or silicon oxides, including lithiumsilicon-oxide.

The thickness of the ion conducting layer 10 will vary depending on thematerial. In some embodiments using an inorganic ion conductor the ionconducting layer 10 is about 250 nm to 1 nm thick, preferably about 50nm to 5 nm thick. In some embodiments using an organic ion conductor,the ion conducting layer is about 100000 nm to 1000 nm thick or about25000 nm to 10000 nm thick. The thickness of the ion conducting layer isalso substantially uniform. In one embodiment, a substantially uniformion conducting layer varies by not more than about +/−10% in each of theaforementioned thickness ranges. In another embodiment, a substantiallyuniform ion conducting layer varies by not more than about +/−5% in eachof the aforementioned thickness ranges. In another embodiment, asubstantially uniform ion conducting layer varies by not more than about+/−3% in each of the aforementioned thickness ranges.

Referring again to FIG. 1, substrates 24 and 25 have flat surfaces. Thatis, they have a surface coincides with the tangential plane in eachpoint. Although substrates with flat surfaces are typically employed forelectrochromic architectural windows and many other electrochromicdevices, it is contemplated that the multi-layer devices of the presentinvention may have a single or even a doubly curved surface. Stateddifferently, it is contemplated that each of the layers of stack 28 havea corresponding radius of curvature. See, for example, U.S. Pat. No.7,808,692 which is incorporated herein by reference in its entirety withrespect to the definition of single and doubly curved surfaces andmethods for the preparation thereof.

FIG. 4 depicts a cross-sectional structural diagram of an electrochromicdevice according to a second embodiment of the present invention. Movingoutward from the center, electrochromic device 101 compriseselectrochromic electrode layer 120. On either side of electrochromicelectrode layer 120 are first and second electrically conductive layers122, 123 which, in turn, are arranged against outer substrates 124, 125.Elements 122, 120, and 123 are collectively referred to as anelectrochromic stack 128. Electrically conductive layer 122 is inelectrical contact with a voltage source via bus bar 126 andelectrically conductive layer 123 is in electrical contact with avoltage source via bus bar 127 whereby the transmittance ofelectrochromic device 120 may be changed by applying a voltage pulse toelectrically conductive layers 122, 123. The pulse causes a cathodiccompound in electrochromic electrode layer 120 to undergo a reversiblechemical reduction and an anodic compound in electrochromic electrodelayer 120 to undergo a reversible chemical oxidation. Either thecathodic or anodic compound will demonstrate electrochromic behaviorsuch that electrochromic electrode layer 120 becomes less transmissiveor more transmissive after the pulse; in one embodiment, electrochromicdevice 101 has relatively greater transmittance before the voltage pulseand lesser transmittance after the voltage pulse or vice versa.

FIG. 20 depicts a cross-sectional structural diagram of anelectrochromic device according to a third embodiment of the presentinvention. Moving outward from the center, electrochromic device 301comprises ion conductor layer 310. Electrochromic electrode layer 320 ison one side of and in contact with a first surface of ion conductorlayer 310. A first electrically conductive layer 322 is in contact withelectrochromic layer 320. A second electrically conductive layer 323 ison a second surface of ion conductor layer 310, the first and secondsurfaces of ion conductor layer 310 being opposing surfaces. The firstand second electrically conductive layers 322, 323 are arranged againstouter substrates 324, 325. Elements 310, 320, 322 and 323 arecollectively referred to as electrochromic stack 328. Electricallyconductive layer 322 is in electrical contact with a voltage source (notshown) via bus bar 326 and electrically conductive layer 323 is inelectrical contact with a voltage source (not shown) via bus bar 327whereby the transmittance of electrochromic layer 320 may be changed byapplying a voltage pulse to electrically conductive layers 322, 323. Ionconductor layer 310 comprises a species that is capable of reversiblyoxidizing or reducing upon the insertion or withdrawal of electrons orions and this species may also be electrochromically active. The voltagepulse causes electrons and ions to move between first electrode layer320 and ion conducting layer 310 and, as a result, electrochromicmaterials in the electrode layer 320 changes color, thereby makingelectrochromic device 301 less transmissive or more transmissive. In oneembodiment, electrochromic device 301 has relatively greatertransmittance before the voltage pulse and relatively lessertransmittance after the voltage pulse or vice versa.

In general, the composition and sheet resistance profiles for first andsecond electrically conductive layers 122, 123, 322, 323 are aspreviously described in connection with FIG. 1. Electrochromic electrodelayers 120 and 320 may, for example, contain an electrochromic material,either as a solid film or dispersed in an electrolyte, theelectrochromic material being selected from among inorganic metal oxidessuch as tungsten trioxide (WO₃), nickel oxide (NiO) and titanium dioxide(TiO₂), and organic electrochromic materials including bipyridinium salt(viologen) derivatives, N,N′-di(p-cyanophenyl) 4,4′-bipyridilium (CPQ),quinone derivatives such as anthraquinone and azine derivatives such asphenothiazine.

In operation, to switch an electrochromic device of the presentinvention from a first to a second optical state having differingtransmissivities, i.e., from a state of relatively greatertransmissivity to a state of lesser transmissivity or vice versa, avoltage pulse is applied to the electrical contacts/bus bars on thedevice. Once switched, the second optical state will persist for sometime after the voltage pulse has ended and even in the absence of anyapplied voltage; for example, the second optical state will persist forat least 1 second after the voltage pulse has ended and even in theabsence of any applied voltage. By way of further example, the secondoptical state may persist for at least 5 seconds after the voltage pulsehas ended and even in the absence of any applied voltage. By way offurther example, the second optical state may persist for at least 1minute after the voltage pulse has ended and even in the absence of anyapplied voltage. By way of further example, the second optical state maypersist for at least 1 hour after the voltage pulse has ended and evenin the absence of any applied voltage. The device may then be returnedfrom the second optical state to the first optical state by reversingthe polarity and applying a second voltage pulse and, upon beingswitched back, the first optical state will persist for some time afterthe second pulse has ended even in the absence of any applied voltage;for example, the first optical state will persist for at least 1 secondafter the voltage pulse has ended and even in the absence of any appliedvoltage. By way of further example, the first optical state may persistfor at least 1 minute after the voltage pulse has ended and even in theabsence of any applied voltage. By way of further example, the firstoptical state may persist for at least 1 hour after the voltage pulsehas ended and even in the absence of any applied voltage. This processof reversibly switching from a first persistent to a second persistentoptical state, and then back again, can be repeated many times andpractically indefinitely.

In some embodiments the waveform of the voltage pulse may be designed sothat the local voltage across the electrochromic stack never exceeds apre-determined level; this may be preferred, for example, in certainelectrochromic devices where excessive voltage across the electrochromicstack can damage the device and/or induce undesirable changes to theelectrochromic materials.

Advantageously, the non-uniform sheet resistance of the first and/orsecond electrically conductive layers of the multi-layer devices of thepresent invention may permit greater tolerances with respect to themagnitude and/or duration of the voltage pulse. As a result, the localvoltage across the electrochromic stack may be significantly less thanthe voltage applied across the entire device because of the voltage dropin the electrically conductive layer(s). For example, in one embodiment,the applied potential across the electrochromic stack has a magnitude ofat least 2 Volts. By way of further example, the voltage pulse may havea magnitude of at least 3 Volts. By way of further example, the voltagepulse may have a magnitude of at least 4 Volts. By way of furtherexample, the voltage pulse may have a magnitude of at least 5 Volts. Byway of further example, the voltage pulse may have a magnitude of atleast 6 Volts. By way of further example, the voltage pulse may have amagnitude of at least 7 Volts. By way of further example, the voltagepulse may have a magnitude of at least 8 Volts. By way of furtherexample, the voltage pulse may have a magnitude of at least 9 Volts. Byway of further example, the voltage pulse may have a magnitude of atleast 10 Volts. By way of further example, the voltage pulse may have amagnitude of at least 11 Volts. By way of further example, the voltagepulse may have a magnitude of at least 12 Volts. By way of furtherexample, the voltage pulse may have a magnitude of at least 13 Volts. Byway of further example, the voltage pulse may have a magnitude of atleast 14 Volts. By way of further example, the voltage pulse may have amagnitude of at least 15 Volts. By way of further example, the voltagepulse may have a magnitude of at least 16 Volts. By way of furtherexample, the voltage pulse may have a magnitude of at least 18 Volts. Byway of further example, the voltage pulse may have a magnitude of atleast 20 Volts. By way of further example, the voltage pulse may have amagnitude of at least 22 Volts. By way of further example, the voltagepulse may have a magnitude of at least 24 Volts. In general, suchpotentials may be applied for a relatively long period of time. Forexample, a potential having a magnitude of any of such values may beapplied for a period of at least 1 seconds. By way of further example, apotential having a magnitude of any of such values may be applied for aperiod of at least 10 seconds. By way of further example, a potentialhaving a magnitude of any of such values may be applied for a period ofat least 20 seconds. By way of further example, a potential having amagnitude of any of such values may be applied for a period of at least40 seconds.

To illustrate for one specific exemplary embodiment, a voltage pulse of16 volts may be applied across an electrochromic stack incorporating twoTCO electrically conductive layers having non-uniform sheet resistanceand a bus bar located at opposite perimeter edges of the entire device.The voltage pulse rises quick to allow the local voltage drop across thelayers to quickly ramp to 1.0 volts and maintain that voltage until thedevice switching approaches completeness at which point the devicelayers begin to charge up and the current drops. Because of the gradientand sheet resistance in the electrically conductive layers the voltagedrop across the device is constant across the device and in addition,there is a voltage drop across each of the electrically conductivelayers of the device. The voltage drops through the non-uniformresistivity electrically conductive layers enables a voltagesignificantly larger than the maximum operating voltage of the devicestack to be applied across the entire assembly and maintain a localvoltage across the device stack below a desired value. As the devicecharging takes place, the applied voltage is dropped to keep the localvoltage across the device layers at 1.0 volts. The voltage pulse willdrop to a steady state value close to 1 volt if it is desired to keep asteady state 1.0 volts across the local device thickness oralternatively the voltage pulse will drop to zero volts if it is desiredto keep no voltage across the local device thickness in steady state.

To change the optical state of a multilayer device to an intermediatestate, a voltage pulse is applied to the electrical contacts/bus bars onthe device. This shape of this voltage pulse would typically be devicespecific and depend on the intermediate state desired. The intermediatestate can be defined in terms of a total charge moved, charge state ofdevice, or an optical measurement of the device. By using non-uniformelectron conductor layers to apply uniform local voltages across thedevice layers this provides a unique advantage for rapid large areaintermediate state control using optical state feedback since a localoptical measurement of the device state near the edge will berepresentative of the entire device at all times (no iris effect). Alsoby using non-uniform electron conductor layers to apply uniform localvoltages across the device layers this provides a unique advantage forrapid large area intermediate state control using voltage feedback sincethe voltage state at the bus bars will be representative of the entiredevice rather than an average across a non-uniformly colored device(again no iris effect). In a specific example, a voltage pulse of 32volts is applied across an electrochromic device incorporating twogradient TCO layers and a bus bar located at opposite perimeter edges ofthe entire device. The voltage pulse rises quick to allow the localvoltage drop across the layers to quickly ramp to 1.0 volts and maintainthat voltage until the device reaches a desired optical state measuredwith an appropriate optical sensor at which point the voltage pulsequickly ramps down to zero or to a desired steady state voltage.

Having described the invention in detail, it will be apparent thatmodifications and variations are possible without departing the scope ofthe invention defined in the appended claims. Furthermore, it should beappreciated that all examples in the present disclosure are provided asnon-limiting examples.

EXAMPLES

The following non-limiting examples are provided to further illustratethe present invention. It should be appreciated by those of skill in theart that the techniques disclosed in the examples that follow representapproaches the inventors have found function well in the practice of theinvention, and thus can be considered to constitute examples of modesfor its practice. However, those of skill in the art should, in light ofthe present disclosure, appreciate that many changes can be made in thespecific embodiments that are disclosed and still obtain a like orsimilar result without departing from the spirit and scope of theinvention.

Example 1: Iris Effect Switching

A 1-D lumped element circuit model has been used to simulate the dynamicbehavior of an electrochromic type device using component valuesappropriate to capture the switching dynamics of a large area device.The lumped element model shown in FIG. 5 is based on a paper bySkrayabin et. al. (Electrochimica Acta 44 (1999) 3203-3209). Theelectrochromic device is locally modeled by a parallel resistor andnon-linear capacitor and the electrically conducting layer is locallymodeled as a resistor. A network of these devices as shown in FIG. 5models the behavior of a large area electrochromic device. A lowresistance resistor between the device and the power supply simulatesthe contact resistance between the power supply and the device. FIG. 6shows the applied voltage, a 1.1 volt step function. The resultantcurrent flow is shown in FIG. 7; it rises rapidly to a maximum value andthen decreases as the device switching takes place. FIG. 8 shows thevoltage drop across the electrochromic device near the edge of thedevice, part way toward the center, and near the center of the devicefrom both sides of the device (six traces total). What is seen is thatthe edge of the device switches relatively slowly and moving towards thecenter of the device the switching occurs even more slowly. The slowerswitching of the center of the device relative to the edge is the wellunderstood characteristic of large area devices referred to as the iriseffect.

The switching speed of this entire device can be increased by applying amore complex voltage waveform. Such a waveform along with its effect onthe current and effect on switching dynamics is shown in FIGS. 9-11. Theapplied voltage pulse was selected to ramp up the voltage near the edgeto a maximum, not to exceed 1.0 volts. This required that the voltagewaveform quickly ramp up and then decrease the voltage in time as neededto keep the voltage across the device below 1.0 volts. This waveform isshown in FIG. 9. The current flowing out of the power supply is shown inFIG. 10 and shows a sharp initial current increase followed by adecreasing current over time following the decrease in applied voltage.FIG. 11 shows the voltage drop across the device near the edge of thedevice, part way towards the center of the device, and near the middleof the device from both contacts (6 traces in total). It can be seenthat the device in this case switches near the edge of the device muchfaster than in the previous example, where the applied voltage was astep function. Near the center of the device the switching is still slowand while the whole device switches faster than in the previous case,the iris effect may be exacerbated as the voltage difference between theedge and the center is larger during part of the switching. Note thatthe switching is symmetric such that the curves corresponding to pointslocated symmetrically opposite on the device switch identically andoverlap. This iris effect can be reduced or eliminated by adjusting thesheet resistance distribution in the electron conductor layers of themulti-layer device as shown in the next example.

Example 2: Uniform Switching

The 1-D circuit model shown in FIG. 12 embodies a constant gradient insheet resistance in each of the electrically conducting layers. Theseare arranged such that the sheet resistance is lowest near theconnection the power supply and highest at the opposite end of thedevice. One polarity of the power supply is applied to one electricallyconducting layer and the other polarity of the power supply is appliedto the opposing electrically conducting layer and at the opposite sidesof the device. With this arrangement there is no iris effect andswitching behavior is qualitatively different—providing both uniformswitching across the entire device and much faster switching of theentire device. This switching behavior is shown in FIGS. 13-15. FIG. 13shows the applied voltage waveform. This waveform was selected to limitthe voltage across the device to always be below a desired threshold (inthis example 1.0 volts). The resultant waveform is a voltage pulse witha fast rising leading edge and a slower falling edge selected to keepthe voltage across the device below but near the desired thresholdvoltage. FIG. 14 shows the current flowing through the device as afunction of time, the current ramps up quickly and has a waveformsimilar in shape to that of the applied voltage pulse. FIG. 15 shows thevoltage drop across the electrochromic device at the edge of the devicenear the power supply contact and near the center of the device. As canbe seen in this plot, the voltage profile across the device is the sameat all locations. The result is that significant current can be driventhrough the device in a relatively short period of time while thevoltage across the device is low and the same everywhere. Such anon-uniform sheet resistance in the electrically conducting layers canallow large area electrochromic devices to switch with dynamics similarto those of small area devices.

Example 3: Directional Switching

The lumped element model in FIG. 16 is an example of a configurationthat provides a controlled switching profile in an electrochromicdevice. In this case, the device will switch from left to right. Theelectrically conducting layers are asymmetric. The top electricallyconducting layer is a layer with sheet resistance of 5Ω/□ the left sideand linearly increasing to 50Ω/□ at the right side of this layer. Thebottom electrically conducting layer is a layer with sheet resistance of30Ω/□ at the left side and linearly decreasing to 3Ω/□ at the right sideof the layer. FIG. 17 shows the applied voltage waveform to product arapidly rising voltage at the left side of the device while keeping thisvoltage across the device below 1.0 volts. FIG. 18 shows thecorresponding current through the device which initially rapidlyincreases then quickly falls as the device switches. FIG. 19 shows thevoltage across the device at six location from left to right. As can beseen, the voltage increases and approaches 1.0V at the far left side thefastest and at each point further right the voltage across the deviceincreases and approaches 1.0V more slowly. This will result in a devicethat will switch from left to right in a pre-determined manner. Thisbehavior can be controlled at window sizes that would exhibit an iriseffect with a given constant sheet resistance in the electricallyconducting layers. In addition the rate at which the apparent velocityof switching occurs from left to right can be controlled by thedifference between the sheet resistance profiles in the electricallyconducting layers. For example, if the lower electrically conductinglayer in Example 3 was a layer with sheet resistance of 40Ω/□ at theleft side and linearly decreasing to 4Ω/□ at the right side of the layerthen the switching of the device in this case would be much faster fromleft to right. In the limiting case that that the sheet resistanceprofiles are linear and identical in opposing directions then the devicewill switch uniformly as demonstrated in Example 2.

Example 4 and Comparative Example 4A

All substrates for Example 4 and Comparative Example 4A (and Examples5-7 and comparative examples), were 9×13.7 cm in dimension and between2.3 and 4 mm thick.

Devices containing a single electrochromic electrode layer and a singleion conductor layer positioned between two electrically conductivelayers located between two outer substrates of glass were prepared forthe example and comparative example. Electrically conductive layers weretin doped indium oxide (ITO) transparent conductive oxide (TCO) layerssputter-coated on float glass substrates. Comparative Example 4A usedITO coated substrates with a uniform sheet resistance of 65Ω/□. Example4 used ITO coated substrate with a linear increase in sheet resistancefrom 70-400Ω/□. The sheet resistance increased linearly in the 13.7 cmdirection (i.e., a constant sheet resistance gradient) and wasapproximately uniform in the 9 cm direction. The ITO substrates werecustom prepared for the work by sputtering onto bare float glasssubstrates. The procedure for fabrication of the devices is detailedbelow.

The sheet resistance of the ITO coated substrates was measured using a4-point probe measurement tool. Sheet resistance measurements on thegradient resistance ITO substrates were made on at least at five equallyspaced locations placed on a straight line with the line runningperpendicular to the 9 cm sides of the substrate and with the measuredlocations covering the majority of the sheet resistance gradient.

A tungsten oxide precursor was prepared as follows. In a 0° C. ice bath,a 2 L flask was charged with 40 mL water and fitted with a stir bar.Then 800 mL of a 50:50 solution of aqueous hydrogen peroxide (30 wt. %H₂O₂) and glacial acetic acid was added and stirred 30 minutes toequilibrate to the ice bath temperature. To the cold mixture, 65 g oftungsten metal was added and stirred to react for 24 hours. Theresulting solution was filtered through coarse (Whatman 54) and thenfine (Whatman 42) filter paper to yield a clear, slightly yellowfiltrate. The filtrate was then refluxed 18 hours at 55° C. andrefiltered through fine (Whatman 42) filter paper, then dried undervacuum (using a water aspirator) at 65° C. to recover a powderedtungsten peroxy acid ester product.

The coating solution was prepared by dissolving 18 g of the solidtungsten peroxy acid precursor, 0.668 g lithium methoxide, and 2.367 goxalic acid dehydrate in 60 mL anhydrous ethanol under an argonatmosphere in a glove box.

The coating solution was spin-coated onto the two TCO types (uniformsheet resistance and gradient sheet resistance).

Following coating, a strip of the coated film was removed from all sidesof the substrate using water. This exposed the underlying TCO forelectrical contacts and better adhesion. The films were processed withthe following program in a humidity chamber.

Step Temperature ° C. Relative Humidity (%) Time (min) 1 26 40 5 2 30 8010 3 45 70 15 4 60 65 15 5 90 10 10 6 105 1 10 7 25 25 19

After removal from the humidity chamber, the films were processed in anoven in air with the following program to produce a tungsten oxide film.

Step Temperature ° C. Time (min) 1 Ambient 0 2 Ramp to 240 60 3 240 60 4Ambient 60

Final thickness was measured by a contact profilometer to beapproximately 300 nm.

Two holes 4 mm in diameter were drilled into opposite corners of a setof ITO substrates (one uniform sheet resistance ITO and one gradientsheet resistance ITO). The devices were then constructed by hermeticallysealing matching substrates together using thermal-set epoxy around theoutside edge with the conductive surfaces facing inward (e.g., twouniform sheet resistance ITO substrates were used in a single devicewhile two gradient sheet resistance ITO substrates were used in anotherdevice). A fixed gap width of 210 μm was set by mixing glass beads witha known diameter into the epoxy. The substrates were shifted relative toeach other to produce an overlap of approximately 0.5 cm in alldirections to permit electrical connections and electrical measurements.Busbars for electrical contact were soldered onto the overlappingsections on the short sides of the device (i.e., 9 cm sides). Thegradient ITO device was assembled with the gradients opposing each otherand with their low sheet resistance sides serving as the busbar area forcontacts (i.e., the low sheet resistance side of each substrate wasaligned to face the high sheet resistance side of the other and both lowsides positioned to be exposed.)

The prepared devices were filled through the drilled holes with an ionconductor solution of 0.5 M lithium triflate and 0.05 M ferrocene inanhydrous propylene carbonate. The holes were then sealed. In thesedevices the ferrocene in the ion conductor layer acts as a speciescapable of reversibly oxidizing and reducing upon the insertion orwithdraw of electrons.

Analysis and characterization of the completed devices was carried outusing a custom lab instrument. The instrument permitted simultaneouscontrol of the voltage source, measurement of transmission across theelectromagnetic spectrum at various points in the device, and voltagepotential across the electrochemical stack at various points. Thisallows full characterization of the device and links voltage potentialin the electrochromic stack at a particular point in the device toelectromagnetic transmission at that same point. For example, a devicecould be characterized with a pre-set voltage pulse profile and simplemeasurement of voltage and optical data. Additionally, the device couldbe characterized with the voltage pulse adjusting to maintain a targetvoltage potential in the electrochromic stack.

The devices of Comparative Example 4A and Example 4 were characterized.Data showing variations in voltage and transmission values are presentedbelow. The “Iris” value is the maximum difference in transmission at 550nm between an area near the edge and the center of the device measuredwhile switching the device from bleached to colored states. The MaximumVoltage A is the maximum difference in voltage potential across theelectrochromic stack near the edge and the center of the device whileswitching the device from bleached to colored states. The source voltagewas automatically adjusted to maintain 1.2 volts across theelectrochromic stack at the edge of the device. Total time to steadystate was approximately 150 seconds in each case.

Maximum Iris Value Maximum Voltage Δ (ΔT at 550 nm) Comparative 0.64 V31% Example 4 Example 4 0.25 V 6%

Example 5 and Comparative Example 5A

Devices comprising two electrochromic electrode layers, positioned oneach side of a single ion conductor layer with each electrochromicelectrode layer positioned against an electrically conductive TCO layerand with each TCO layer arranged against an outer substrate of glasswere prepared for the example and comparative example. ComparativeExample 5A used ITO coated substrates with a uniform sheet resistance ofapproximately 220Ω/□. Example 5 used ITO coated substrates with aconstant gradient in sheet resistance from approximately 100-500Ω/□. Thegradient device was constructed with the substrates oriented as inExample 4. The ITO was custom sputter deposited for the project and thenthermally processed to increase its sheet resistance. Sheet resistancemeasurements were taken on deposited electrode films following thermalprocessing and just prior to insertion into a final device.

The sheet resistance of the ITO coated substrates was measured using a4-point probe measurement tool. Sheet resistance measurements on theuniform ITO coated substrates were made at several points on the film.Sheet resistance measurements on the gradient sheet resistance ITOsubstrates were made on at least five equally spaced locations on astraight line with the line running perpendicular and between the two 9cm sides of the substrate. It was observed that the sheet resistance ofthe ITO would vary due to thermal treatment and application of anelectrode film. A correction factor was applied to the sheet resistancemeasurements after thermal treatment or application of an electrodefilm. The correction factor was calculated by measuring the overallsheet resistance of the substrate between two points placed at themid-point of each 9 cm side and offset from the edge by approximately0.5 cm and ensuring measurement on exposed TCO. The correction factorwas then the ratio of this overall sheet resistance of the substratefrom before and after the treatment. For example, if this sheetresistance increased from 100Ω to 150Ω due to a thermal treatment andthe original measured sheet resistance in Ω/□ was 200Ω/□ then thereported sheet resistance in Ω/sq after thermal treatment was 300 Ω/□.

Tungsten oxide films were prepared as in Example 4 on the two substratetypes (i.e., one uniform sheet resistance and one gradient sheetresistance substrate). The tungsten oxide films served as the firstelectrode layers.

Complimentary vanadium oxide xerogel films were prepared on the twosubstrate types. Two holes 4 mm in diameter were drilled into oppositecorners of this set before coating. The vanadium oxide films served asthe second electrode layer.

The vanadium oxide xerogel coating proceeds by acidification of LiVO₃ bycation exchange followed promptly by spin coating before gelation of theresulting vanadic acid can occur. The procedure for the coating solutionis as follows.

A 2 M LiVO₃ precursor solution was prepared by dissolving 8.08 g LiVO₃in 34 mL 40% vol aqueous ethanol by stirring at 60° C. for 1 hour. Thecloudy solution was filtered (Whatman 40), and the filter rinsed with40% ethanol. The filtrate was diluted to 40 mL and shaken to mixyielding a slightly yellow, viscous 2 M LiVO₃ solution.

The flash ion exchange columns were prepared by packing 2 mL (3.4 meq)of Dowex WX8 100-200 mesh cation exchange resin (proton form) into a 3mL syringe fitted with a 0.2 micron PTFE Acrodisk filter to retain theresin beads. The columns were rinsed twice with water and then drained.One milliliter of the LiVO₃ solution was added to a packed syringe,which was shaken ten seconds to mix into the resin. The “column” waseluted by depressing the syringe plunger and the bright orange vanadicacid solution was immediately refiltered (0.2 micron PTFE Acrodisk) ontothe substrate and spun to form the coating. Following coating, a stripof the coated film was removed from all sides of the substrate using awater treatment. This exposed the underlying TCO for electrical contactsand better adhesion.

The resulting films were thermally processed using the following recipeto produce a vanadium oxide film.

Step # Procedure Time 1 Heat 25° C. to 240° C. 60 minutes 2 Hold at 240°C. 60 minutes 3 Cool 240° C. to 40° C. 120 minutes 

Final thickness was measured by a contact profilometer to beapproximately 100 nm.

The vanadium oxide films were lithiated in a glove box using a lithiummetal counter-electrode and a solution of 1 M lithium perchlorate inpropylene carbonate. A two-step procedure involving oxidation to 3.8Vfollowed by reduction at 2.4 V was performed with the voltages quotedversus reference lithium metal. Lithiation was performed to put thevanadium oxide into a state of reduction that allows it to serve as thecounter-electrode to the tungsten oxide films.

The devices were then constructed by hermitically sealing matchingsubstrates together using an acrylic adhesive tape with the conductivesurfaces facing inward. A fixed gap width of 500 μm was set by theadhesive tape. Acrylic adhesive tape was used for rapid device creation.The substrates were shifted relative to each other to produce an overlapof approximately 0.5 cm in all directions to permit electricalconnections and measurements. The gradient device was assembled as inExample 4 with the low sheet resistance sides exposed for electricalcontact.

The prepared devices were filled through the drilled holes with anelectrolyte solution of 1.5 M Lithium Bis(trifluoromethanesulfonyl)imidein anhydrous propylene carbonate. The holes were then sealed.

The Example 5 and Comparative Example 5A devices were analyzed with thecustom setup described in Example 4. The results are shown below

Switching time (bleached Maximum Iris Value (ΔT Source voltage tocolored) Voltage Δ at 550 nm) Comparative Example  150 seconds 1.4 V 17%5A. Electrochemical stack at edge of device controlled to 1.2 V Example5. <100 Seconds 0.3 V 6% Electrochemical stack at edge of devicecontrolled to 1.2 V

As demonstrated by the results, the device of Example 5 significantlymitigated the Iris value while achieving a faster switching speed thanthe device of Comparative Example 5A.

Example 6

A device was prepared containing two electrochromic electrode layers,positioned on each side of a single ion conductor layer with eachelectrochromic electrode layer positioned against an electricallyconductive TCO layer and with each TCO layer arranged against an outersubstrate of glass. The device of this example 6 used TEC 70 substrates(Pilkington) with two laser scribed patterns. TEC glass is commerciallyavailable fluorine doped tin oxide (FTO) where the number in the nameindicates the sheet resistance in Ω/□. FTO is a TCO. The laser scribedpatterns increase and modulate the sheet resistance of the TCO. Thefirst TEC substrate had a laser pattern that simulated a uniform sheetresistance of 250Ω/□. The second TEC substrate had a laser scribepattern that simulated a linear increase in sheet resistance from170-1500Ω/□ substrate.

The sheet resistance of scribed TEC glass substrates was calculated bymeasuring the sheet resistance between two points spaced one cm apart onthe substrate. The same measurement was performed on a set of un-scribedTEC glass with a known sheet resistance value in Ω/□. From theun-scribed TEC measurements a calibration curve was calculated relatingΩ/□ to the 2-point sheet resistance value. A sheet resistance value inΩ/□ was then calculated for each measurement on the scribed TEC glasssubstrates. The second TEC glass substrate sheet resistance profile wasmeasured by taking individual measurements at 1 cm intervals in astraight line between and perpendicular to the two 9 cm sides of thesubstrate.

The device should be compared with Example 3. Example 3 describes alumped element model of an electrochromic device with a directionalswitch. This directional switch is achieved in Example 3 by an asymmetryin the electrically conductive layer (e.g., the TCO). The device ofExample 6 has an asymmetry in the two electrically conductive layers andwas expected to show a directional switch where the device switchesfaster on the low sheet resistance side of the second TEC substrate andslower on the high sheet resistance side of the second TEC substrate.

The device was constructed using the procedure described below.

The tungsten oxide film was prepared as in Example 4 on the second TECsubstrate (with gradient sheet resistance). The tungsten oxide filmserved as the first electrode layer.

A complementary vanadium oxide film was prepared on the first TECsubstrate (uniform sheet resistance). The vanadium oxide film served asthe second electrode layer. Two holes approximately 4 mm in diameterwere drilled into opposite corners of the uniform sheet resistancesubstrate before coating. The coating solution was prepared according tothe following recipe.

A solution of LiVO₃ was prepared by dissolving the solid in 5% wtsolution in water at 60° C., followed by filtration through Whatman 40paper. The vanadate species were protonated to “vanadic acid” by runningthis 5% wt solution of LiVO₃ dropwise through an ion exchange columnpacked with at least 20 equivalents of Dowex Monosphere 650 C in H⁺form, eluting with additional deionized water until a pale yellowendpoint. The eluted vanadic acid was allowed to stand overnight, afterwhich it was sonicated to disperse any solids that had formed.

Six equivalents of triethylamine were added to the vanadic acid and themixture was sonicated at 40-50° C. for one hour to form a colorless,slightly turbid. This solution was evaporated under reduced pressure atup to 55° C. to yield a yellow viscous liquid. This was dissolved inethanol or 2-methoxyethanol to between 0.4 M vanadium and 1.2 M vanadiumto yield a final coating solution.

The coating solution was spin-coated onto the substrate. Followingcoating, a strip of the coated film was removed from all sides of thesubstrate using a water treatment. This exposed the underlying TCO forelectrical contacts and better adhesion. The film was thermallyprocessed using the following recipe in air to produce a vanadium oxidefilm.

Step # Procedure Time 1 Heat 25° C. to 350° C. 60 minutes 2 Hold at 350°C. 60 minutes 3 Cool 350° C. to 40° C. 120 minutes 

Final thickness was measured by a contact profilometer to beapproximately 200 nm.

The vanadium oxide film was lithiated in a glove box using a lithiummetal counterelectrode and a 1 M solution of lithium perchlorate inpropylene carbonate. The voltage during lithiation was 2.7 to 2.9 voltsversus lithium metal. Lithiation was performed to put the vanadium oxideinto a state of reduction that allows it to serve as thecounter-electrode to the tungsten oxide film.

The devices were then constructed by hermitically sealing matchingsubstrates together using thermal setting epoxy around the outside edgewith the conductive surfaces facing inward. A fixed gap width of 210 μmwas set by mixing glass beads of a known diameter into the epoxy. Thesubstrates were shifted relative to each other to produce an overlap ofapproximately 0.5 cm in all directions to permit electrical connectionsand measurements. The device was constructed with the gradient substrateoriented with the low sheet resistance side exposed for electricalconnection.

The prepared devices were hydrated in a humidity chamber at 25% relativehumidity at 25° C. for 2 hours. The prepared devices were then filledthrough the drilled holes with an electrolyte solution of 1.5 M LithiumBis(trifluoromethane-sulfonyl)imide in anhydrous propylene carbonate.The holes were then sealed.

The device of Example 6 was characterized and demonstrated a pronounceddirectional change effect where the device switched from bleached tocolored states substantially faster on the low sheet resistance side ofthe second TEC substrate than the high sheet resistance side of thesecond TEC substrate. The difference in transmission exceeded 25% duringcoloration. This directional change qualitatively agreed with theprediction made in Example 3.

Example 7 and Comparative Example 7A

Devices were made containing two electrode one of which beingelectrochromic, positioned on each side of a single ion conductor layerwith each electrode layer positioned against an electrically conductiveTCO layer and with each TCO layer arranged against an outer substrate ofglass. The device of Comparative Example 7A used TEC 70 substrates(Pilkington) with a laser scribed pattern to simulate 250Ω/□ sheetresistance. The laser scribed patterns increase and modulate the sheetresistance of the TCO. The device of Example 7 used TEC 70 substrateswith a laser scribed pattern that simulated a 70-250Ω/□ substrate. Sheetresistance values were calculated as in Example 6. The device wasconstructed with the substrates oriented with opposing sheet resistancegradients as in Example 4. All devices were constructed using theprocedure described below.

A 20 wt % colloidal dispersion of cerium oxide coating solution in anaqueous solution (Alfa Aesar) was spin-coated onto a set of the laserscribed FTO substrates. Following spin-coating, a strip of the ceriumoxide film was removed from all sides using an acetic acid solution(aq., 2.5 wt %). The film was thermally processed for one hour at 240°C. in air.

Final thickness was measured by profilometry to be approximately 350 nm.

The cerium oxide films served as the first electrode layer.

Complementary vanadium oxide films were prepared on the same set ofsubstrates. The vanadium oxide films served as the second electrodelayer and is electrochromic. Two holes 4 mm in diameter were drilledinto the corners of this set before coating. The vanadium solution wasprepared according to the following procedure.

A 2 M LiVO₃ precursor solution was prepared by dissolving 8.08 g LiVO₃in 34 mL 40% vol aqueous ethanol by stirring at 60° C. for 1 hour. Thecloudy solution was filtered (Whatman 40), and the filter rinsed with40% ethanol. The filtrate was diluted to 40 mL and shaken to mixyielding a slightly yellow, viscous 2 M LiVO₃ solution.

Twenty milliliters of this LiVO₃ solution was acidified by the additionof between 4.5 and 6 g Dowex Monosphere 650 C cation exchange resin(proton form) under vigorous stirring. The resulting bright orangemixture was filtered through filter paper (Whatman 40) and then dilutedwith 6.6 mL water to yield the final coating solution.

The coated films were thermally processed one hour at 240° C. in air toyield a vanadium oxide film. Final thickness was measured by a contactprofilometer to be approximately 150 nm.

The vanadium oxide films were lithiated in a glove box using a lithiummetal counterelectrode and a solution of 1 M lithium perchlorate inpropylene carbonate. A two-step procedure involving oxidation to 3.8Vfollowed by reduction at 2.4 V was performed with the voltages quotedversus reference lithium metal. Lithiation was performed to put thevanadium oxide into a state of reduction that allows it to serve as thecounter-electrode to the cerium oxide films.

The devices were then constructed by hermitically sealing matchingsubstrates together using acrylic adhesive tape around the outside edgewith the conductive surfaces facing inward. A fixed gap width of 500 μmwas set by the adhesive tape. The substrates were shifted relative toeach other to produce an overlap of approximately 0.5 cm in alldirections to permit electrical connections and measurements. Thegradient device was assembled as in Example 4 with the low sheetresistance sides exposed for electrical contact.

The prepared devices were then filled through the drilled holes with anelectrolyte solution of 1.5 M Lithium Bis(trifluoromethanesulfonyl)imidein anhydrous propylene carbonate. The holes were then sealed.

The Iris Value for these devices was measured at 450 nm. This wavelengthwas used as it showed a larger change in transmittance between thebleached and colored states than 550 nm.

Iris Switching time Value (bleached to Maximum (ΔT at Source voltagecolored) Voltage Δ 450 nm) Comparative Example 7A. >180 seconds 1.6 V 6%Electrochemical stack at edge of device controlled to 2 V. Example 7.Electrochemical  75 seconds 0.3 V 3% stack at edge of device controlledto 2 V.

The gradient device achieved more uniform switching and significantlyfaster switching speed.

What is claimed is:
 1. A method of forming an electrochromic multilayerstack comprising: providing a first substrate comprising a firsttransparent electrically conductive layer; patterning the firsttransparent electrically conductive layer with laser patterning to forma patterned first transparent electrically conductive layer having afirst spatially varying resistance to the flow of electrical currentthrough the first transparent electrically conductive layer that variesas a function of position in the first transparent electricallyconductive layer, and forming a first electrode layer comprising anelectrochromic material over the patterned first transparentelectrically conductive layer.
 2. The method of claim 1, whereinpatterning the first transparent electrically conductive layer compriseslaser patterning a series of laser scribes.
 3. The method of claim 1,wherein depositing the first transparent electrically conductive layeron the substrate comprises forming a film having a constant thicknessand a constant resistivity.
 4. The method of claim 1, wherein patterningthe first transparent electrically conductive layer varies the firstspatially varying resistance such that a ratio of a value of a maximumsheet resistance to a value of minimum sheet resistance in the firstelectrically conductive layer is at least
 10. 5. The method of claim 1,further comprising: providing a second substrate comprising a secondtransparent electrically conductive layer and patterning the secondtransparent electrically conductive layer with laser patterning to forma patterned second transparent electrically conductive layer having asecond spatially varying resistance to the flow of electrical currentthrough the second transparent electrically conductive layer that variesas a function of position in the second transparent electricallyconductive layer; forming a second electrode layer over the patternedsecond transparent electrically conductive layer, forming an ionconductor layer between the first and the second electrode layers toform an electrochromic multilayer device.
 6. The method of claim 5,wherein the first spatially varying resistance varies as a function ofposition opposite to that of the second spatially varying resistance.